Data processing apparatus and data processing method as well as encoding apparatus and encoding method

ABSTRACT

A data processing apparatus, a data processing method, an encoding apparatus and an encoding method which can be applied, for example, to a transmission system for transmitting an LDPC code and so forth, and which can improve the tolerance to errors. Of an LDPC code which is prescribed in the DVB-S.2 and has a code length of 64,800 and an encoding rate of 2/3, mb code bits are replaced, and the code bits after the replacement become symbol bits of b symbols. When m is 8 and b is 2, where the i+1th bit from the most significant bit of 8×2 code bits and 8×2 symbol bits of two successive symbols are represented by b i  and y i , respectively, replacement of allocating b 0  to y 15 , b 1  to y 7 , b 2  to y 1 , b 3  to y 5 , b 4  to y 6 , b 5  to y 13 , b 6  to y 11 , b 7  to y 9 , b 8  to y 8 , b 9  to y 14 , b 10  to y 12 , b 11  to y 3 , b 12  to y 0 , b 13  to y 10 , b 14  to y 4  and b 15  to y 2 .

TECHNICAL FIELD

This invention relates to a data processing apparatus and a dataprocessing method as well as an encoding apparatus and an encodingmethod, and particularly to a data processing apparatus and a dataprocessing method as well as an encoding apparatus and an encodingmethod which can improve, for example, the tolerance to errors.

The LDPC (Low Density Parity Check) code has a high error correctioncapacity and, in recent years, begins to be adopted widely intransmission systems including satellite digital broadcasting systemssuch as, for example, the DVB (Digital Video Broadcasting)-S.2 systemused in Europe (refer to, for example, Non-Patent Document 1). Further,it is investigated to adopt the LDPC code also in terrestrial digitalbroadcasting of the next generation.

It is being found by recent research that a performance proximate to theShannon limit is provided by the LDPC code as the code length isincreased similarly to a turbo code and so forth. Further, since theLDPC code has a property that the minimum distance increases inproportion to the code length, it has a characteristic that it has asuperior block error probability characteristic. Also it is advantageousthat a so-called error floor phenomenon which is observed in a decodingcharacteristic of the turbo code and so forth little occurs.

In the following, such an LDPC code as described above is describedparticularly. It is to be noted that the LDPC code is a linear code, andalthough it is not necessarily be a two-dimensional code, the followingdescription is given under the assumption that it is a two-dimensionalcode.

The LDPC code has the most significant characteristic in that a paritycheck matrix which defines the LDPC code is a sparse matrix. Here, thesparse matrix is a matrix in which the number of those elements whosevalue is “1” is very small (matrix in which almost all elements are 0).

FIG. 1 shows an example of a parity check matrix H of an LDPC code.

In the parity check matrix H of FIG. 1, the weight of each column(column weight) (number of “1”) (weight) is “3” and the weight of eachrow (row weight) is “6.”

In encoding by LDPC codes (LDPC encoding), for example, a generatormatrix G is produced based on a parity check matrix H and this generatormatrix G is multiplied by two-dimensional information bits to produce acodeword (LDPC code).

In particular, an encoding apparatus which carries out LDPC encodingfirst calculates a generator matrix G which satisfies an expressionGH^(T)=0 together with a transposed matrix H^(T) of a parity checkmatrix H. Here, if the generator matrix G is a K×N matrix, then theencoding apparatus multiplies the generator matrix G by a bit string(vector u) of K information bits to produce a codeword c (=uG) of Nbits. The codeword (LDPC code) produced by the encoding apparatus isreceived by the reception side through a predetermined communicationpath.

Decoding of the LDPC code can be carried out using an algorithm proposedas probabilistic decoding (Probabilistic Decoding) by the Gallager, thatis, a message passing algorithm by belief propagation on a so-calledTanner graph including a variable node (also called message node) and acheck node. In the following description, each of the variable node andthe check node is suitably referred to simply as node.

FIG. 2 illustrates a procedure of decoding of an LDPC code.

It is to be noted that, in the following description, a real numbervalue where the “0” likelihood in the value of the nth code bit of anLDPC code (one codeword) received by the reception side is representedin a log likelihood ratio is suitably referred to as reception valueu_(Oi). Further, a message outputted from a check node is represented byu_(j) and a message outputted from a variable node is represented byv_(i).

First, in decoding of an LDPC code, as seen in FIG. 2, an LDPC code isreceived and a message (check node message) u_(j) is initialized to “0”and besides a variable k which assumes an integer as a counter ofrepeated processes is initialized to “0” at step S11, whereafter theprocessing advances to step S12. At step S12, mathematical operationrepresented by an expression (1) (variable node mathematical operation)is carried out based on the reception value u_(Oi) obtained by thereception of the LDPC code to determine a message (variable nodemessage) v_(i). Further, mathematical operation represented by anexpression (2) (check node mathematical operation) is carried out basedon the message v_(i) to determine the message u_(j).

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 1} \right\rbrack & \; \\{v_{i} = {u_{oi} + {\sum\limits_{j = 1}^{d_{v} - 1}\; u_{j}}}} & (1) \\\left\lbrack {{Expression}\mspace{14mu} 2} \right\rbrack & \; \\{{\tanh\left( \frac{u_{j}}{2} \right)} = {\prod\limits_{i = 1}^{d_{c} - 1}\;{\tanh\left( \frac{v_{i}}{2} \right)}}} & (2)\end{matrix}$

Here, d_(v) and d_(c) in the expression (1) and the expression (2) areparameters which can be selected arbitrarily and represent the number of“1s” in a vertical direction (column) and a horizontal direction (row)of the parity check matrix H. For example, in the case of a (3, 6) code,d_(v)=3 and d_(c)=6.

It is to be noted that, in the variable node mathematical operation ofthe expression (1) and the check node mathematical operation of theexpression (2), the range of the mathematical operation is 1 to d_(v)−1or 1 to d_(c)−1 because a massage inputted from an edge (lineinterconnecting a variable node and a check node) from which a messageis to be outputted is not made an object of the mathematical operation.Meanwhile, the check node mathematical operation of the expression (2)is carried out by producing in advance a table of a function R(v₁, v₂)represented by an expression (3) defined by one output with respect totwo inputs v₁ and v₂ and using the table successively (recursively) asrepresented by an expression (4).

[Expression 3]x=2 tan h ⁻¹{tan h(v ₁/2)tan h(v ₂/2)}=R(v ₁ ,v ₂)  (3)[Expression 4]u _(j) =R(v ₁ ,R(v ₂ ,R(v ₃ , . . . R(v _(d) _(c) ⁻² ,v _(d) _(c)⁻¹))))  (4)

At step S12, the variable k is incremented by “1” further, and theprocessing advances to step S13. At step S13, it is decided whether ornot the variable k is higher than a predetermined repeated decoding timenumber C. If it is decided at step S13 that the variable k is not higherthan C, then the processing returns to step S12, and similar processingis repeated thereafter.

On the other hand, if it is decided at step S13 that the variable k ishigher than C, then the processing advances to step S14, at which amessage v_(i) as a decoding result to be outputted finally by carryingout mathematical operation represented by an expression (5) isdetermined and outputted, thereby ending the decoding process of theLDPC code.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 5} \right\rbrack & \; \\{v_{i} = {u_{oi} + {\sum\limits_{j = 1}^{d_{v}}\; u_{j}}}} & (5)\end{matrix}$

Here, the mathematical operation of the expression (5) is carried out,different from the variable node mathematical operation of theexpression (1), using messages u_(j) from all edges connecting to thevariable node.

FIG. 3 illustrates an example of the parity check matrix H of a (3, 6)LDPC code (encoding rate: 1/2, code length: 12).

In the parity check matrix H of FIG. 3, the weight of a column is 3 andthe weight of a row is 6 similarly as in FIG. 1.

FIG. 4 shows a Tanner graph of the parity check matrix H of FIG. 3.

Here, in FIG. 4, a check node is represented by “+,” and a variable nodeis represented by “=.” A check node and a variable node correspond to arow and a column of the parity check matrix H, respectively. Aconnection between a check node and a variable node is an edge andcorresponds to “1” of an element of the parity check matrix.

In particular, where the element in the jth row of the ith column of theparity check matrix is 1, the ith variable node (node of “=”) from aboveand the jth check node (node of “+”) from above are connected by anedge. The edge represents that a code bit corresponding to the variablenode has a constraint condition corresponding to the check node.

In the sum product algorithm (Sum Product Algorithm) which is a decodingmethod for LDPC codes, variable node mathematical operation and checknode mathematical cooperation are carried out repetitively.

FIG. 5 illustrates the variable node mathematical operation carried outwith regard to a variable node.

With regard to the variable node, a message v_(i) corresponding to anedge to be calculated is determined by variable node mathematicaloperation of the expression (1) which uses messages u₁ and u₂ from theremaining edges connecting to the variable node and the reception valueu_(Oi). Also a message corresponding to any other edge is determinedsimilarly.

FIG. 6 illustrates the check node mathematical operation carried out ata check node.

Here, the check node mathematical operation of the expression (2) can becarried out by rewriting the expression (2) into an expression (6) usingthe relationship of an expressiona×b=exp{ln(|a|)+ln(|b|)}×sign(a)×sign(b). It is to be noted that sign(x)is 1 where x≧0 but is −1 where x<0.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 6} \right\rbrack & \; \\\begin{matrix}{u_{j} = {2\;{\tanh^{- 1}\left( {\prod\limits_{i = 1}^{d_{c} - 1}\;{\tanh\left( \frac{v_{i}}{2} \right)}} \right)}}} \\{= {2\;{\tanh^{- 1}\left\lbrack {\exp\left\{ {\sum\limits_{i = 1}^{d_{c} - 1}{{In}\left( {{\tanh\left( \frac{v_{i}}{2} \right)}} \right)}} \right\} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\mspace{14mu}\left( {\tanh\left( \frac{v_{i}}{2} \right)} \right)}}} \right\rbrack}}} \\{= {2\;{\tanh^{- 1}\left\lbrack {\exp\left\{ {- \left( {\sum\limits_{i = 1}^{d_{c} - 1}\;{- {{In}\left( {\tanh\left( \frac{v_{i}}{2} \right)} \right)}}} \right)} \right\}} \right\rbrack} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\mspace{14mu}\left( v_{i} \right)}}}}\end{matrix} & (6)\end{matrix}$

Further, if, where x≧0, a function φ(x) is defined as an expressionφ(x)=ln(tan h(x/2)), then since an expression φ⁻¹(x)=2 tan h⁻¹(e^(−x))is satisfied, the expression (6) can be transformed into an expression(7).

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 7} \right\rbrack & \; \\{u_{j} = {{\phi^{- 1}\left( {\sum\limits_{i = 1}^{d_{c} - 1}{\phi\left( {v_{i}} \right)}} \right)} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\mspace{14mu}\left( v_{i} \right)}}}} & (7)\end{matrix}$

At the check node, the check node mathematical operation of theexpression (2) is carried out in accordance with the expression (7).

In particular, at the check node, the message u_(j) corresponding to theedge to be calculated is determined by check node mathematical operationof the expression (7) using messages v₁, v₂, v₃, v₄ and v₅ from theremaining edges connecting to the check node. Also a messagecorresponding to any other edge is determined in a similar manner.

It is to be noted that the function φ(x) of the expression (7) can berepresented also as φ(x)=ln((e^(x)+1)/(e^(x)−1)), and where x>0,φ(x)=φ⁻¹(x). When the functions φ(x) and φ⁻¹(x) are incorporated inhardware, while they are sometimes incorporated using an LUT (Look UpTable), such LUTs become the same LUT.

Non-Patent Document 1: DVB-S.2: ETSI EN 302 307 V1.1.2 (2006-06)

DISCLOSURE OF INVENTION Technical Problem

The LDPC code is adopted in DVB-S.2 which is a standard for satellitedigital broadcasting and DVB-T.2 which is a standard for terrestrialdigital broadcasting of the next generation. Further, it is planned toadopt the LDPC code in DVB-C.2 which is a standard for CATV (CableTelevision) digital broadcasting of the next generation.

In digital broadcasting in compliance with a standard for DVB such asDVB-S.2, an LDPC code is converted (symbolized) into symbols oforthogonal modulation (digital modulation) such as QPSK (QuadraturePhase Shift Keying), and the symbols are mapped to signal points andtransmitted.

In symbolization of an LDPC code, replacement of code bits of the LDPCcode is carried out in a unit of two or more bits, and code bits aftersuch replacement are determined as bits of a symbol.

While various methods have been proposed as a method for replacement ofcode bits for symbolization of an LDPC code, proposal of a method whichfurther improves the tolerance to various errors in comparison withmethods proposed already is demanded.

Further, also with regard to the LDPC code itself, proposal of an LDPCcode which improves the tolerance to errors in comparison with the LDPCcodes prescribed in DVB standards such as the DVB-S.2 standard isdemanded.

The present invention has been made taking such a situation as describedabove into consideration and makes it possible to improve the toleranceto errors.

Technical Solution

A data processing apparatus or a data processing method of a firstaspect of the present invention is a data processing apparatus or a dataprocessing method, wherein, where code bits of an LDPC (Low DensityParity Check) code having a code length of N bits are written in acolumn direction of storage means for storing the code bits in a rowdirection and the column direction and m bits of the code bits of theLDPC code read out in the row direction are set as one symbol, andbesides a predetermined positive integer is represented by b, thestorage means stores mb bits in the row direction and stores N/(mb) bitsin the column direction, the code bits of the LDPC code being written inthe column direction of the storage means and read out in the rowdirection, the data processing apparatus including replacement means foror a replacing step of replacing, where the mb code bits read out in therow direction of the storage means set as b symbols, the mb code bitssuch that the code bits after the replacement form the symbol bitsrepresentative of the symbols, the LDPC code being an LDPC code which isprescribed in the DVB-S.2 or DVB-T.2 standard and which has a codelength N of 64,800 and has an encoding rate of 2/3, the m bits being 8bits while the integer b is 2, the 8 bits of the LDPC code being mappedas one symbol to ones of 256 signal points prescribed in 256QAM, thestorage means having 16 columns for storing 8×2 bits in the rowdirection and storing 64,800/(8×2) bits in the column direction, thereplacement means carrying out, where the i+1th bit from the mostsignificant bit of the 8×2 code bits read out in the row direction ofthe storage means is represented as bit b_(i) and the i+1th bit from themost significant bit of the 8×2 symbol bits of two successive symbols isrepresented as bit y_(i), replacement for allocating the bit b₀ to thebit y₁₅, the bit b₁ to the bit y₇, the bit b₂ to the bit y₁, the bit b₃to the bit y₅, the bit b₄ to the bit y₆, the bit b₅ to the bit y₁₃, thebit b₆ to the bit y₁₁, the bit b₇ to the bit y₉, the bit b₈ to the bity₈, the bit b₉ to the bit y₁₄, the bit b₁₀ to the bit y₁₂, the bit b₁₁to the bit y₃, the bit b₁₂ to the bit y₀, the bit b₁₃ to the bit y₁₀,the bit b₁₄ to the bit y₄, and the bit b₁₅ to the bit y₂.

In such a first aspect as described above, the LDPC code is an LDPC codewhich is prescribed in the DVB-S.2 or DVB-T.2 standard and which has acode length N of 64,800 and has an encoding rate of 2/3, and the m bitsare 8 bits while the integer b is 2. The 8 bits of the LDPC code aremapped as one symbol to ones of 256 signal points prescribed in 256QAM.The storage means has 16 columns for storing 8×2 bits in the rowdirection and stores 64,800/(8×2) bits in the column direction. In thisinstance, where the i+1th bit from the most significant bit of the 8×2code bits read out in the row direction of the storage means isrepresented as bit b_(i) and the i+1th bit from the most significant bitof the 8×2 symbol bits of two successive symbols is represented as bity_(i), replacement for allocating the bit b₀ to the bit y₁₅, the bit b₁to the bit y₇, the bit b₂ to the bit y₁, the bit b₃ to the bit y₅, thebit b₄ to the bit y₆, the bit b₅ to the bit y₁₃, the bit b₆ to the bity₁₁, the bit b₇ to the bit y₉, the bit b₈ to the bit y₈, the bit b₉ tothe bit y₁₄, the bit b₁₀ to the bit y₁₂, the bit b₁₁ to the bit y₃, thebit b₁₂ to the bit y₀, the bit b₁₃ to the bit y₁₀, the bit b₁₄ to thebit y₄, and the bit b₁₅ to the bit y₂, is carried out.

An encoding apparatus or an encoding method of a second aspect of thepresent invention is an encoding apparatus or an encoding method,including encoding means for or an encoding step of carrying outencoding by an LDPC code which has a code length of 64,800 bits and anencoding rate of 2/3, a parity check matrix of the LDPC code beingconfigured such that elements of the value 1 of an information matrix,which corresponds to the code length of the parity check matrix and aninformation length corresponding to the encoding rate, decided by aparity check matrix initial value table representative of the positionsof the elements of the value 1 of the information matrix are arranged ina period of every 360 columns in the column direction, the parity checkmatrix initial value table being formed from

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In such a second aspect as described above, encoding by an LDPC codewhose code length is 64,800 bits and whose encoding rate is 2/3 iscarried out. The parity check matrix of the LDPC code is configured suchthat elements of the value 1 of an information matrix, which correspondsto the code length of the parity check matrix and an information lengthcorresponding to the encoding rate, decided by a parity check matrixinitial value table representative of the positions of the elements ofthe value 1 of the information matrix are arranged in a period of every360 columns in the column direction. The parity check matrix initialvalue table is formed from

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It is to be noted that the data processing apparatus may be anindependent apparatus or may be an internal block which composes oneapparatus.

ADVANTAGEOUS EFFECT

According to the present invention, the tolerance to errors can beimproved.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a view illustrating a parity check matrix H of an LDPC code.

FIG. 2 is a flow chart illustrating a decoding procedure of an LDPCcode.

FIG. 3 is a view illustrating an example of a parity error matrix of anLDPC code.

FIG. 4 is a view showing a Tanner graph of a parity check matrix.

FIG. 5 is a view showing a variable node.

FIG. 6 is a view showing a check node.

FIG. 7 is a view showing an example of a configuration of an embodimentof a transmission system to which the present invention is applied.

FIG. 8 is a block diagram showing an example of a configuration of atransmission apparatus 11.

FIG. 9 is a view illustrating a parity check matrix.

FIG. 10 is a view illustrating a parity matrix.

FIG. 11 is a view illustrating a parity check matrix of an LDPC code andcolumn weights prescribed in the DVB-S.2 standard.

FIG. 12 is a view illustrating a signal point arrangement of 16QAM.

FIG. 13 is a view illustrating a signal point arrangement of 64QAM.

FIG. 14 is a view illustrating a signal point arrangement of 64QAM.

FIG. 15 is a view illustrating a signal point arrangement of 64QAM.

FIG. 16 is a view illustrating processing of a demultiplexer 25.

FIG. 17 is a view illustrating processing of the demultiplexer 25.

FIG. 18 is a view showing a Tanner graph regarding decoding of an LDPCcode.

FIG. 19 is a view showing a parity matrix H_(T) having a staircasestructure and a Tanner graph corresponding to the parity matrix H_(T).

FIG. 20 is a view showing the parity matrix H_(T) of a parity checkmatrix H corresponding to the LDPC code after parity interleaving.

FIG. 21 is a view illustrating a conversion parity check matrix.

FIG. 22 is a view illustrating processing of a column twist interleaver24.

FIG. 23 is a view illustrating column numbers of a memory 31 necessaryfor the column twist interleaving and addresses of writing startingpositions.

FIG. 24 is a view illustrating column numbers of the memory 31 necessaryfor the column twist interleaving and addresses of writing startingpositions.

FIG. 25 is a flow chart illustrating a transmission process.

FIG. 26 is a view showing a model of a communication path adopted in asimulation.

FIG. 27 is a view illustrating a relationship between an error rateobtained by the simulation and a Doppler frequency f_(d) of a flutter.

FIG. 28 is a view illustrating a relationship between an error rateobtained by the simulation and a Doppler frequency f_(d) of a flutter.

FIG. 29 is a block diagram showing an example of a configuration of anLDPC encoding section 21.

FIG. 30 is a flow chart illustrating a process of LDPC encoding section.

FIG. 31 is a view illustrating a parity check matrix initial value tableof an encoding rate of 2/3 and a code length of 16,200.

FIG. 32 is a view illustrating a parity check matrix initial value tableof an encoding rate of 2/3 and a code length of 64,800.

FIG. 33 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 2/3 and the code length of 64,800.

FIG. 34 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 2/3 and the code length of 64,800.

FIG. 35 is a view illustrating a parity check matrix initial value tableof an encoding rate of 3/4 and a code length of 16,200.

FIG. 36 is a view illustrating a parity check matrix initial value tableof an encoding rate of 3/4 and a code length of 64,800.

FIG. 37 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 3/4 and the code length of 64,800.

FIG. 38 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 3/4 and the code length of 64,800.

FIG. 39 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 3/4 and the code length of 64,800.

FIG. 40 is a view illustrating a parity check matrix initial value tableof an encoding rate of 4/5 and a code length of 16,200.

FIG. 41 is a view illustrating a parity check matrix initial value tableof an encoding rate of 4/5 and a code length of 64,800.

FIG. 42 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 4/5 and the code length of 64,800.

FIG. 43 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 4/5 and the code length of 64,800.

FIG. 44 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 4/5 and the code length of 64,800.

FIG. 45 is a view illustrating a parity check matrix initial value tableof an encoding rate of 5/6 and a code length of 16,200.

FIG. 46 is a view illustrating a parity check matrix initial value tableof an encoding rate of 5/6 and a code length of 64,800.

FIG. 47 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 5/6 and the code length of 64,800.

FIG. 48 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 5/6 and the code length of 64,800.

FIG. 49 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 5/6 and the code length of 64,800.

FIG. 50 is a view illustrating a parity check matrix initial value tableof an encoding rate of 8/9 and a code length of 16,200.

FIG. 51 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 8/9 and the code length of 64,800.

FIG. 52 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 8/9 and the code length of 64,800.

FIG. 53 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 8/9 and the code length of 64,800.

FIG. 54 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 8/9 and the code length of 64,800.

FIG. 55 is a view illustrating a parity check matrix initial value tableof an encoding rate of 9/10 and a code length of 64,800.

FIG. 56 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 9/10 and the code length of 64,800.

FIG. 57 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 9/10 and the code length of 64,800.

FIG. 58 is a view illustrating the parity check matrix initial valuetable of the encoding rate of 9/10 and the code length of 64,800.

FIG. 59 is a view illustrating a method of determining a parity checkmatrix H from a parity check matrix initial table.

FIG. 60 is a view illustrating a replacement process in accordance withthe existing methods.

FIG. 61 is a view illustrating a replacement process in accordance withthe existing methods.

FIG. 62 is a view illustrating code bit groups and symbol bit groupswhere an LDPC code having a code length of 64,800 and an encoding rateof 2/3 is modulated by 256QAM and the multiple b is 2.

FIG. 63 is a view illustrating an allocation rule where an LDPC codehaving a code length of 64,800 and an encoding rate of 2/3 is modulatedby 256QAM and the multiple b is 2.

FIG. 64 is a view illustrating replacement of code bits in accordancewith the allocation rule where an LDPC code having a code length of64,800 and an encoding rate of 2/3 is modulated by 256QAM and themultiple b is 2.

FIG. 65 is a view illustrating BERs where a replacement process of a newreplacement method and where a replacement process of an existing methodis carried out.

FIG. 66 is a view illustrating an example of a parity check matrixinitial value table for an LDPC code whose E_(b)/N₀ as a performancethreshold value is better than that of a standard code.

FIG. 67 is a view illustrating the example of the parity check matrixinitial value table for an LDPC code whose E_(b)/N₀ as a performancethreshold value is better than that of the standard code.

FIG. 68 is a view illustrating the example of the parity check matrixinitial value table for an LDPC code whose E_(b)/N₀ as a performancethreshold value is better than that of the standard code.

FIG. 69 is a view illustrating relationships of the E_(s)/N₀ and the BERregarding the standard code and a proposed code.

FIG. 70 is a block diagram showing an example of a configuration of areception apparatus 12.

FIG. 71 is a flow chart illustrating a reception process.

FIG. 72 is a view illustrating an example of a parity check matrix of anLDPC code.

FIG. 73 is a view illustrating a matrix (conversion parity check matrix)obtained by applying row replacement and column replacement to a paritycheck matrix.

FIG. 74 is a view illustrating a conversion parity check matrix dividedinto a unit of 5×5 bits.

FIG. 75 is a block diagram showing an example of a configuration of adecoding apparatus in which node mathematical operation is carried outcollectively for P nodes.

FIG. 76 is a block diagram showing an example of a configuration of aLDPC decoding section 56.

FIG. 77 is a block diagram showing an example of a configuration of anembodiment of a computer to which the present invention is applied.

FIG. 78 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 2/3 and a code length of16,200.

FIG. 79 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 2/3 and a code length of64,800.

FIG. 80 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 2/3 and the code length of64,800.

FIG. 81 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 2/3 and the code length of64,800.

FIG. 82 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 3/4 and a code length of16,200.

FIG. 83 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 3/4 and a code length of64,800.

FIG. 84 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 3/4 and the code length of64,800.

FIG. 85 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 3/4 and the code length of64,800.

FIG. 86 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 3/4 and the code length of64,800.

FIG. 87 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 4/5 and a code length of16,200.

FIG. 88 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 4/5 and a code length of64,800.

FIG. 89 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 4/5 and the code length of64,800.

FIG. 90 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 4/5 and the code length of64,800.

FIG. 91 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 4/5 and the code length of64,800.

FIG. 92 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 5/6 and a code length of16,200.

FIG. 93 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 5/6 and a code length of64,800.

FIG. 94 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 5/6 and the code length of64,800.

FIG. 95 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 5/6 and the code length of64,800.

FIG. 96 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 5/6 and the code length of64,800.

FIG. 97 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 8/9 and a code length of16,200.

FIG. 98 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 8/9 and the code length of64,800.

FIG. 99 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 8/9 and the code length of64,800.

FIG. 100 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 8/9 and the code length of64,800.

FIG. 101 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 8/9 and the code length of64,800.

FIG. 102 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 9/10 and a code length of64,800.

FIG. 103 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 9/10 and the code length of64,800.

FIG. 104 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 9/10 and the code length of64,800.

FIG. 105 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 9/10 and the code length of64,800.

FIG. 106 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 1/4 and a code length of64,800.

FIG. 107 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 1/4 and the code length of64,800.

FIG. 108 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 1/3 and a code length of64,800.

FIG. 109 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 1/3 and the code length of64,800.

FIG. 110 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 2/5 and a code length of64,800.

FIG. 111 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 2/5 and the code length of64,800.

FIG. 112 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 1/2 and a code length of64,800.

FIG. 113 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 1/2 and the code length of64,800.

FIG. 114 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 1/2 and the code length of64,800.

FIG. 115 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 3/5 and a code length of64,800.

FIG. 116 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 3/5 and the code length of64,800.

FIG. 117 is a view illustrating the example of the parity check matrixinitial value table of the encoding rate of 3/5 and the code length of64,800.

FIG. 118 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 1/4 and a code length of16,200.

FIG. 119 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 1/3 and a code length of16,200.

FIG. 120 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 2/5 and a code length of16,200.

FIG. 121 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 1/2 and a code length of16,200.

FIG. 122 is a view illustrating an example of a parity check matrixinitial value table of an encoding rate of 3/5 and a code length of16,200.

FIG. 123 is a view illustrating another example of the parity checkmatrix initial value table of the encoding rate of 3/5 and the codelength of 16,200.

FIG. 124 is a view illustrating a method of determining a parity checkmatrix H from a parity check matrix initial table.

FIG. 125 is a view illustrating an example of replacement of code bits.

FIG. 126 is a view illustrating another example of replacement of codebits.

FIG. 127 is a view illustrating a further example of replacement of codebits.

FIG. 128 is a view illustrating a still further example of replacementof code bits.

FIG. 129 is a view illustrating a simulation result of the BER.

FIG. 130 is a view illustrating another simulation result of the BER.

FIG. 131 is a view illustrating a further simulation result of the BER.

FIG. 132 is a view illustrating a still simulation result of the BER.

FIG. 133 is a view illustrating an example of replacement of code bits.

FIG. 134 is a view illustrating another example of replacement of codebits.

FIG. 135 is a view illustrating a further example of replacement of codebits.

FIG. 136 is a view illustrating a still further example of replacementof code bits.

FIG. 137 is a view illustrating a yet further example of replacement ofcode bits.

FIG. 138 is a view illustrating a yet further example of replacement ofcode bits.

FIG. 139 is a view illustrating a yet further example of replacement ofcode bits.

FIG. 140 is a view illustrating a yet further example of replacement ofcode bits.

FIG. 141 is a view illustrating a yet further example of replacement ofcode bits.

FIG. 142 is a view illustrating a yet further example of replacement ofcode bits.

FIG. 143 is a view illustrating a yet further example of replacement ofcode bits.

FIG. 144 is a view illustrating a yet further example of replacement ofcode bits.

FIG. 145 is a view illustrating processing of a multiplexer 54 whichcomposes a deinterleaver 53.

FIG. 146 is a view illustrating processing of a column twistdeinterleaver 55.

FIG. 147 is a block diagram showing another example of a configurationof the reception apparatus 12.

FIG. 148 is a block diagram showing a first example of a configurationof a reception system which can be applied to the reception apparatus12.

FIG. 149 is a block diagram showing a second example of theconfiguration of the reception system which can be applied to thereception apparatus 12.

FIG. 150 is a block diagram showing a third example of the configurationof the reception system which can be applied to the reception apparatus12.

EXPLANATION OF REFERENCE SYMBOLS

11 Transmission apparatus, 12 Reception apparatus, 21 LDPC encodingsection, 22 Bit interleaver, 23 Parity interleaver, 24 Column twistinterleaver, 25 Demultiplexer, 26 Mapping section, 27 Orthogonalmodulation section, 31 Memory, 32 Replacement section, 51 Orthogonaldemodulation section, 52 Demapping section, 53 Deinterleaver, 54Multiplexer, 55 Column twist deinterleaver, 56 LDPC decoding section,300 Edge data storage memory, 301 Selector, 302 Check node calculationsection, 303 Cyclic shift circuit, 304 Edge data storage memory, 305Selector, 306 Reception data memory, 307 Variable node calculationsection, 308 Cyclic shift circuit, 309 Decoded word calculation section,310 Reception data re-arrangement section, 311 Decoded datare-arrangement section, 601 Encoding processing block, 602 Storageblock, 611 Encoding rate setting portion, 612 Initial value tablereading out portion, 613 Parity check matrix production portion, 614Information bit reading out portion, 615 Encoding parity mathematicaloperation portion, 616 Control portion, 701 Bus, 702 CPU, 703 ROM, 704RAM, 705 Hard disk, 706 Outputting section, 707 Inputting section, 708Communication section, 709 Drive, 710 Input/output interface, 711Removable recording medium, 1001 Reverse replacement section, 1002Memory, 1011 Parity deinterleaver, 1021 LDPC decoding section, 1101Acquisition section, 1101 Transmission line decoding processing section,1103 Information source decoding processing section, 1111 Outputtingsection, 1121 Recording section

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 7 shows an example of a configuration of an embodiment of atransmission system to which the present invention is applied (the termsystem signifies a logical aggregate of a plurality of apparatusirrespective of whether or not the individual component apparatus areincluded in the same housing).

Referring to FIG. 7, the transmission system includes a transmissionapparatus 11 and a reception apparatus 12.

The transmission apparatus 11 carries out, for example, transmission(broadcast) (transfer) of a television broadcasting program. That is,the transmission apparatus 11, for example, encodes object data whichare an object of transmission such as image data, sound data and soforth as a television broadcasting program into an LDPC code andtransmits the resultant data through, for example, a communication path13 such as a satellite channel, ground waves and CATV network.

The reception apparatus 12 is, for example, a tuner, a televisionreceiver or a STB (Set Top Box) for receiving a television broadcastingprogram or PC (Personal Computer) for receiving IPTV (Internet ProtocolTelevision), and receives LDPC codes transmitted thereto from thetransmission apparatus 11 through a communication path 13, decodes theLDPC codes into object data and outputs the object data.

Here, it has been known that LDPC codes utilized in the transmissionsystem in FIG. 7 exhibit a very high capacity in an AWGN (Additive WhiteGaussian Noise) communication path.

However, in the communication path 13 such as ground waves, burst errorsor erasure sometimes occurs. For example, in an OFDM (OrthogonalFrequency Division Multiplexing) system, in a multi-path environmentwherein the D/U (Desired to Undesired Ratio) is 0 dB (power ofUndesired=echo is equal to the power of Desired=main path), the power ofa particular symbol becomes zero (erasure) in response to a delay of anecho (paths other than the main path).

Further, also in a flutter (communication path in which an echo whosedelay is zero and to which a Doppler (dopper) frequency is applied isadded), where the D/U is 0 dB, a case wherein the power of an entireOFDM symbol at a specific point of time is reduced to zero (erasure) bythe Doppler frequency occurs.

Further, from a situation of wiring lines on the reception apparatus 12side from a reception section (not shown) such as an antenna or the likefor receiving a signal from the transmission apparatus 11 to thereception apparatus 12 or from instability of the power supply to thereception apparatus 12, burst errors sometimes appear.

Meanwhile, in decoding of LDPC codes, since variable node mathematicaloperation of the expression (1) wherein addition of (reception valuesu_(Oi) of) code bits of an LDPC code as seen in FIG. 5 above describedis carried out in a column of the parity check matrix H and hence avariable node corresponding to a code bit of the LDPC code, if an erroroccurs with the code bit used for the variable node mathematicaloperation, then the accuracy of a message to be determined drops.

Then, since, in decoding of the LDPC code, the message determined at thevariable node connecting to the check node is used to carry out checknode mathematical operation of the expression (7) at the check node, ifthe number of check nodes where (code bits of the LDPC codecorresponding to) a plurality of variable nodes connected theretoexhibit an error (including erasure) at the same time becomes great,then the performance of the decoding deteriorates.

For example, if two or more of the variable nodes connected to the checknode suffer from erasure at the same time, then the check node returns amessage that the probability that the value may be 0 and the probabilitythat the value may be 1 are equal to each other to all variable nodes.In this instance, those check nodes to which the message of the equalprobabilities does not contribute to one cycle of decoding processing(one set of variable node mathematical operation and check nodemathematical operation), and as a result, an increased number of timesof repetition of decoding processing are required. Consequently, theperformance of the decoding deteriorates. Further, the power consumptionof a reception apparatus 12 which carries out decoding of the LDPC codeincreases.

Accordingly, the transmission system shown in FIG. 7 is configured suchthat the tolerance to burst errors or erasure is improved while theperformance in an AWGN communication path is maintained.

FIG. 8 shows an example of a configuration of the transmission apparatus11 of FIG. 7.

Referring to FIG. 8, the transmission apparatus 11 includes an LDPCencoding section 21, a bit interleaver 22, a mapping section 26 and anorthogonal modulation section 27.

To the LDPC encoding section 21, object data are supplied.

The LDPC encoding section 21 carries out LDPC encoding of the objectdata supplied thereto in accordance with a parity check matrix in whicha parity matrix which is a portion corresponding to parity bits of anLDPC code has a staircase structure and outputs an LDPC code wherein theobject data are information bits.

In particular, the LDPC encoding section 21 carries out LDPC encoding ofencoding the object data into an LDPC code prescribed, for example, inthe DVB-S.2 or DVB-T.2 standards and outputs an LDPC code obtained as aresult of the LDPC encoding.

Here, in the DVB-T.2 standard, it is scheduled to adopt the LDPC codesprescribed in the DVB-S.2 standard. The LDPC code prescribed in theDVB-S.2 standard is an IRA (Irregular Repeat Accumulate) code, and theparity matrix in the parity check matrix of the LDPC code has astaircase structure. The parity matrix and the staircase structure arehereinafter described. Further, the IRA code is described, for example,in “Irregular Repeat-Accumulate Codes,” H. Jin., A. Khandekar, and R. J.McEliece, in Proceedings of 2nd International Symposium on Turbo codesand Related Topics, pp. 1-8, September 2000.

The LDPC code outputted from the LDPC encoding section 21 is supplied tothe bit interleaver 22.

The bit interleaver 22 is a data processing apparatus for interleavingdata and includes a parity interleaver 23, a column twist interleaver 24and a demultiplexer (DEMUX) 25.

The parity interleaver 23 carries out parity interleave of interleavingparity bits of the LDPC code from the LDPC encoding section 21 topositions of other parity bits and supplies the LDPC code after theparity interleave to the column twist interleaver 24.

The column twist interleaver 24 carries out column twist interleave forthe LDPC code from the parity interleaver 23 and supplies the LDPC codeafter the column twist interleave to the demultiplexer 25.

In particular, the LDPC code is transmitted after two or more code bitsthereof are mapped to signal points representing one symbol oforthogonal modulation by the mapping section 26 hereinafter described.

The column twist interleaver 24 carries out, for example, such columntwist interleave as hereinafter described as a re-arranging process ofre-arranging code bits of the LDPC code from the parity interleaver 23such that a plurality of code bits of the LDPC code corresponding to thevalue 1 included in one arbitrary row of the parity check matrix used inthe LDPC encoding section 21 are not included in one symbol.

The demultiplexer 25 carries out a replacing process of replacing thepositions of two or more code bits of the LDPC code (which are to be asymbol) from the column twist interleaver 24 to obtain an LDPC codewhose tolerance to AWGN is reinforced. Then, the demultiplexer 25supplies two or more code bits of an LDPC code obtained by thereplacement process as a symbol to the mapping section 26.

The mapping section 26 maps the symbol from the demultiplexer 25 tosignal points determined by a modulation method of orthogonal modulation(multi-value modulation) carried out by the orthogonal modulationsection 27.

In particular, the mapping section 26 maps the LDPC code from thedemultiplexer 25 into a signal point determined by the modulationsystem, on an IQ plane (IQ constellation) defined by an I axisrepresentative of an I component which is in phase with a carrier and aQ axis representative of a Q component which is orthogonal to thecarrier wave.

Here, as the modulation method of orthogonal modulation carried out bythe orthogonal modulation section 27, modulation methods including, forexample, a modulation method defined in the DVB-T standards, that is,for example, QPSK (Quadrature Phase Shift Keying), 16QAM (QuadratureAmplitude Modulation), 64QAM, 256QAM, 1024QAM, 4096QAM and so forth areavailable. What modulation method should be used for orthogonalmodulation to be carried out by the orthogonal modulation section 27 isset in advance, for example, in accordance with an operation of thetransmission apparatus 11 by an operator. It is to be noted that theorthogonal modulation section 27 can carry out some other orthogonalmodulation such as, for example, 4PAM (Pulse Amplitude Modulation).

The symbol mapped to a signal point by the mapping section 26 issupplied to the orthogonal modulation section 27.

The orthogonal modulation section 27 carries out orthogonal modulationof a carrier in accordance with (the symbol mapped to) the signal pointfrom the mapping section 26 and transmits a modulation signal obtainedby the orthogonal modulation through the communication path 13 (FIG. 7).

Now, FIG. 9 illustrates a parity check matrix H used in LDPC encoding bythe LDPC encoding section 21 of FIG. 8.

The parity check matrix H has an LDGM (Low-Density Generation Matrix)structure and can be represented by an expression H=[H_(A)|H_(T)] froman information matrix H_(A) of a portion corresponding to informationbits and a parity matrix H_(T) corresponding to parity bits from amongcode bits of the LDPC code (matrix in which elements of the informationmatrix H_(A) are elements on the left side and elements of the paritymatrix H_(T) are elements on the right side).

Here, the bit number of information bits and the bit number of paritybits from among code bits of one LDPC code (one codeword) are referredto as information length K and parity length M, and the bit number ofcode bits of one LDPC code is referred to as code length N (=K+M).

The information length K and the parity length M regarding an LDPC codeof a certain code length N depend upon the encoding rate. Meanwhile, theparity check matrix H is a matrix whose rows×columns are M×N. Then, theinformation matrix H_(A) is an M×K matrix and the parity matrix H_(T) isan M×M matrix.

FIG. 10 illustrates the parity matrix H_(T) of the parity check matrix Hof an LDPC code prescribed in the DVB-S.2 (and DVB-T.2) standard.

The parity matrix H_(T) of the parity check matrix H of the LDPC codeprescribed in the DVB-S.2 standard has a staircase structure whereinelements of the value 1 are arranged like a staircase as seen in FIG.10. The row weight of the parity matrix H_(T) is 1 with regard to thefirst row but is 2 with regard to all of the remaining rows. Meanwhile,the column weight is 1 with regard to the last column but is 2 withregard to all of the remaining columns.

As described above, the LDPC code of the parity check matrix H whereinthe parity matrix H_(T) has a staircase structure can be producedreadily using the parity check matrix H.

In particular, an LDPC code (one codeword) is represented by a rowvector c and a column vector obtained by transposing the row vector isrepresented by c^(T). Further, a portion of information bits from withinthe row vector c which is an LDPC code is represented by an row vector Aand a portion of parity bits is represented by a row vector T.

Here, in this instance, the row vector c can be presented by anexpression c=[A|T] from the row vector A as information bits and the rowvector T as parity bits (row vector wherein the elements of the rowvector A are elements on the left side and the elements of the rowvector T are elements on the right side).

It is necessary for the parity check matrix H and the row vector c=[A|T]as the LDPC code to satisfy an expression Hc^(T)=0, and where the paritymatrix H_(T) of the parity check matrix H=[H_(A)|H_(T)] has such astaircase structure as shown in FIG. 10, the row vector T as parity bitswhich forms the row vector c=[A|T] which satisfies the expressionHc^(T)=0 can be determined sequentially by successively setting theelements in the rows beginning with the elements in the first row of thecolumn vector Hc^(T) in the expression Hc^(T)=0 to zero.

FIG. 11 illustrates the parity check matrix H of an LDPC code and columnweights defined in the DVB-S.2 (and DVB-T.2) standard.

In particular, FIG. 11A illustrates the parity check matrix H of an LDPCcode defined in the DVB-S.2 standard.

With regard to KX columns from the first column of the parity checkmatrix H, the column weight is X; with regard to succeeding K3 columns,the column weight is 3; with regard to succeeding M−1 rows, the columnweight is 2; and with regard to the last one column, the column weightis 1.

Here, KX+K3+M−1+1 is equal to the code length N.

In the DVB-S.2 standard, the column numbers KX, K3 and M (parity length)as well as the column weight X are prescribed in such a manner as seenin FIG. 11B.

In particular, FIG. 11B illustrates the column numbers KX, K3 and M aswell as the column weight X regarding different encoding rates of LDPCcodes prescribed in the DVB-S.2 standard.

In the DVB-S.2 standard, LDPC codes of the code lengths N of 64,800 bitsand 16,200 bits are prescribed.

And as seen in FIG. 11B, for the LDPC code whose code length N is 64,800bits, 11 encoding rates (nominal rates) 1/4, 1/3, 2/5, 1/2, 3/5, 2/3,3/4, 4/5, 5/6, 8/9 and 9/10 are prescribed, and for the LDPC code whosecode length N is 16,200 bits, 10 encoding rates 1/4, 1/3, 2/5, 1/2, 3/5,2/3, 3/4, 4/5, 5/6 and 8/9 are prescribed.

Regarding LDPC codes, it is known that code bits corresponding to acolumn of the parity check matrix H which has a higher column weightexhibits a lower error rate.

The parity check matrix H prescribed in the DVB-S.2 standard andillustrated in FIG. 11 has a tendency that a column nearer to the headside (left side) has a higher column weight. Accordingly, the LDPC codecorresponding to the parity check matrix H has a tendency that a codebit nearer to the head is higher in tolerance to an error (has a highertolerance to an error) and a code bit nearer to the tail is lower intolerance to an error.

FIG. 12 illustrates an arrangement of (signal points corresponding to)16 symbols on the IQ plane where 16QAM is carried out by the orthogonalmodulation section 27 of FIG. 8.

In particular, FIG. 12A illustrates symbols of 16QAM.

In 16QAM, one symbol represents 4 bits, and 16 (=2⁴) symbols exist.Then, the 16 symbols are disposed such that they form a square shape of4×4 symbols in the I direction×Q direction centered at the origin of theIQ plane.

Now, if the i+1th bit from the most significant bit of the bit stringrepresented by one symbol is represented as bit y_(i), then 4 bitsrepresented by one symbol of 16QAM can be represented as bits y₀, y₁, y₂and y₃ in order beginning with the most significant bit. Where themodulation method is 16QAM, 4 code bits of the LDPC code are set(symbolized) as a symbol (symbol value) of the 4 bits y₀ to y₃.

FIG. 12B indicates bit boundaries regarding the 4 bits (hereinafter, bitis also referred to as symbol bit) y₀ to y₃ represented by the symbol ofthe 16QAM.

Here, a bit boundary regarding a symbol bit y_(i) (in FIG. 12, i=0, 1,2, 3) signifies a boundary between a symbol whose bit y_(i) is 0 andanother symbol whose bit y_(i) is 1.

As seen in FIG. 12B, as regards the most significant symbol bit y₀ fromamong the 4 symbol bits y₀ to y₃ represented by the symbol of 16QAM,only one location of the Q axis on the IQ plane makes a bit boundary,and as regards the second symbol bit y₁ (second from the mostsignificant bit), only one location of the I axis on the IQ plane makesa bit boundary.

Further, as regards the third symbol bit y₃, each of two locationsbetween the first and second columns and between the third and fourthcolumns from the left of the 4×4 symbols makes a boundary.

Furthermore, as regards the fourth symbol bit y₃, each of two locationsbetween the first and second rows and between the third and fourth rowsof the 4×4 symbols makes a boundary.

The symbol bit y₁ represented by a symbol is less likely to becomeerroneous and becomes lower in error probability as the number ofsymbols spaced away from a bit boundary increases but is more likely tobecome erroneous and becomes higher in error probability as the numberof symbols positioned nearer to a bit boundary increases.

If a bit which is less likely to become erroneous (is tolerant to anerror) is referred to as “strong bit” but a bit which is more likely tobecome erroneous (is less tolerant to an error) is referred to as “weakbit,” then as regards the 4 symbol bits y₀ to y₃ represented by symbolsof 16QAM, the most significant symbol bit y₀ and the second symbol bity₁ are strong bits and the third symbol bit y₂ and the fourth symbol bity₃ are weak bits.

FIGS. 13 to 15 illustrate arrangements of (signal points correspondingto) 64 symbols on the IQ plane where 64QAM is carried out by theorthogonal modulation section 27 of FIG. 8.

In 64QAM, one symbol represents 6 bits, and 64 (=2⁶) symbols exist.Then, the 64 symbols are arranged such that they make a square of 8×8symbols in the I direction×Q direction centered at the origin of the IQplane.

The symbol bits represented by one symbol of 64QAM can be represented asbits y₀, y₁, y₂, y₃, y₄, and y₅ in order beginning with the mostsignificant bit. Where the modulation method is 64QAM, 6 code bits ofthe LDPC code are set (symbolized) as a symbol (symbol value) of the 6bits y₀ to y₅.

Here, FIG. 13 indicates bit boundaries regarding the most significantsymbol bit y₀ and the second symbol bit y₁ from among the symbol bits y₀to y₅ of symbols of 64QAM; FIG. 14 indicates bit boundaries regardingthe third symbol bit y₂ and the fourth symbol bit y₃; and FIG. 15indicates bit boundaries regarding the fifth symbol bit y₄ and the sixthsymbol bit y₅.

As seen in FIG. 13, the number of bit boundaries with regard to each ofthe most significant symbol bit y₀ and the second symbol bit y₁ is one.Meanwhile, as seen in FIG. 14, the number of bit boundaries with regardto each of the third symbol bit y₂ and the fourth symbol bit y₃ is two,and as seen in FIG. 15, the number of bit boundaries with regard to eachof the fifth symbol bit y₄ and the sixth symbol bit y₅ is four.

Accordingly, among the symbol bits y₀ to y₅ of symbols of 64QAM, themost significant symbol bit y₀ and the second symbol bit y₁ are thestrongest bits, and the third symbol bit y₂ and the fourth symbol bit y₃are the second strongest bits. Then, the fifth symbol bit y₄ and thesixth symbol bit y₅ are the weakest bits.

From FIG. 12 and further from FIGS. 13 to 15, it can be seen that, asregards symbol bits of symbols of orthogonal modulation, there is atendency that a high-order bit is a strong bit and a low-order bit is aweak bit.

Here, as described hereinabove with reference to FIG. 11, an LDPC codeoutputted from the LDPC encoding section 21 (FIG. 8) includes code bitswhich are tolerant to errors and code bits which are less tolerant toerrors.

Meanwhile, as described hereinabove with reference to FIGS. 12 to 15,symbol bits of symbols of orthogonal modulation carried out by theorthogonal modulation section 27 include strong bits and weak bits.

Accordingly, if a code bit of the LDPC code which is low in tolerance toan error is allocated to a weak symbol bit of a symbol of orthogonalmodulation, then the tolerance to an error drops as a whole.

Therefore, an interleaver has been proposed which interleaves code bitsof an LDPC code such that code bits of the LDPC code which are low intolerance to an error are allocated to strong bits (symbol bits) of asymbol of orthogonal modulation.

The demultiplexer 25 of FIG. 8 carries out processing of theinterleaver.

FIG. 16 is a view illustrating processing of the demultiplexer 25 ofFIG. 8.

In particular, FIG. 16A shows an example of a functional configurationof the demultiplexer 25.

The demultiplexer 25 includes a memory 31 and a replacement section 32.

To the memory 31, an LDPC code from the LDPC encoding section 21 issupplied.

The memory 31 has a storage capacity for storing mb bits in the(horizontal) direction of a row and storing N/(mb) bits in the(vertical) direction of a column. The memory 31 writes code bits of theLDPC code supplied thereto into the column direction and reads out thecode bits in the row direction and then supplies the read out code bitsto the replacement section 32.

Here, N (=information length K+parity length M) represents the codelength of the LDPC code as described hereinabove.

In addition, m represents the bit number of code bits of an LDPC code tobe one symbol, and b is a predetermined positive integer and is amultiple to be used for multiplying m by the integer. The multiplexer 25converts (symbolizes) the code bits of the LDPC code into symbols asdescribed above, and the multiple b represents the number of symbolsobtained in a way by single time symbolization by the multiplexer 25.

FIG. 16A shows an example of a configuration of the demultiplexer 25where the modulation system is 64QAM, and accordingly, the bit number mof code bits of the LDPC code to be one symbol is 6 bits.

Further, in FIG. 16A, the multiple b is 1, and accordingly, the memory31 has a storage capacity of N/(6×1)×(6×1) bits in the columndirection×row direction.

Here, a storage region of the memory 31 which extends in the columndirection and includes one bit in the row direction is hereinafterreferred to suitably as column. In FIG. 16A, the memory 31 includes six(=6×1) columns.

The demultiplexer 25 carries out writing of the code bits of the LDPCcode in a downward direction from above of a column which forms thememory 31 (in a column direction) beginning with a left side columntoward a right side column.

Then, if the writing of the code bits ends with the lowermost bit in therightmost column, then the code bits are read out and supplied to thereplacement section 32 in a unit of 6 bits (mb bits) in the rowdirection beginning with the first row of all of the columns which formthe memory 31.

The replacement section 32 carries out a replacement process ofreplacing the position of code bits of 6 bits from the memory 31 andoutputs the 6 bits obtained by the replacement as 6 symbol bits y₀, y₁,y₂, y₃, y₄ and y₅ representative of one symbol of 64QAM.

In particular, while mb code bits (here, 6 bits) are read out in the rowdirection from the memory 31, if the ith bit (i=0, 1, . . . , mb−1) fromthe most significant bit from among the mb code bits read out from thememory 31 is represented by bit b_(i), then the 6 code bits read out inthe row direction from the memory 31 can be represented as bits b₀, b₁,b₂, b₃, b₄ and b₅ in order beginning with the most significant bit.

A relationship of the column weight described hereinabove with referenceto FIG. 11 leads that the code bit positioned in the direction of thebit b₀ is a code bit high in tolerance to an error while the code bit inthe direction of the bit b₅ is a code bit low in tolerance to an error.

The replacement section 32 carries out a replacement process ofreplacing the position of the 6 code bits b₀ to b₅ from the memory 31such that a code bit which is low in tolerance to an error from amongthe 6 code bits b₀ to b₅ from the memory 31 may be allocated to a bitwhich is high in tolerance from among the symbol bits y₀ to y₅ of onesymbol of 64QAM.

Here, for a replacement method for replacing the 6 code bits b₀ to b₅from the memory 31 so as to be allocated to the 6 symbol bits y₀ to y₅representative of one symbol of 64QAM, various systems have beenproposed.

FIG. 16B illustrates a first replacement method; FIG. 16C illustrates asecond replacement method; and FIG. 16D illustrates a third replacementmethod.

In FIG. 16B to FIG. 16D (similarly also in FIG. 17 hereinafterdescribed), a line segment interconnecting the bits b_(i) and y_(j)signifies that the code bit b_(i) is allocated to the symbol bit y_(j)of the symbol (is replaced into the position of the symbol bit y_(j)).

As the first replacement method, it is proposed to adopt one of threekinds of replacement methods in FIG. 16B, and as the second replacementmethod, it is proposed to adopt one of two kinds of replacement methodsin FIG. 16C.

As the third replacement method, it is proposed to select and use sixkinds of replacement methods in FIG. 16D in order.

FIG. 17 illustrates an example of a configuration of the demultiplexer25 in a case wherein the modulation method is 64QAM (accordingly, thebit number m of code bits of an LDPC code mapped to one symbol is 6similarly as in FIG. 16) and the multiple b is 2, and a fourthreplacement method.

Where the multiple b is 2, the memory 31 has a storage capacity ofN/(6×2)×(6×2) bits in the column direction×row direction and includes 12(=6×2) columns.

FIG. 17A illustrates a writing order of an LDPC code into the memory 31.

The demultiplexer 25 carries out writing of code bits of an LDPC code ina downward direction from above of a column which forms the memory 31(in the column direction) beginning with a left side column toward aright side column as described hereinabove with reference to FIG. 16.

Then, if the writing of code bits ends with the lowermost bit in therightmost column, then the code bits are read out and supplied to thereplacement section 32 in a unit of 12 bits (mb bits) in the rowdirection beginning with the first row of all of the columns which formthe memory 31.

The replacement section 32 carries out a replacement process ofreplacing the position of 12 code bits from the memory 31 in accordancewith the fourth replacement method and outputs the 12 bits obtained bythe replacement as 12 bits representative of two symbols (b symbols) of64QAM, in particular, as 6 symbol bits y₀, y₁, y₂, y₃, y₄ and y₅representative of one symbol of 64QAM and 6 symbol bits y₀, y₁, y₂, y₃,y₄ and y₅ representative of a next one symbol.

Here, FIG. 17B illustrates the fourth replacement method of thereplacement process by the replacement section 32 of FIG. 17A.

It is to be noted that, where the multiple b is 2 (similarly also wherethe multiple b is equal to or higher than 3), in the replacementprocess, mb code bits are allocated to mb symbol bits of b successivesymbols. In the following description including description given withreference to FIG. 17, the i+1th bit from the most significant bit fromamong the mb symbol bits of the b successive symbols is represented asbit (symbol bit) y_(i) for the convenience of description.

Moreover, which replacement method is optimum, that is, whichreplacement method provides improved error rate in an AWGN communicationpath, differs depends upon the encoding rate, code length and modulationmethod of LDPC code and so forth.

Now, parity interleave by the parity interleaver 23 of FIG. 8 isdescribed with reference to FIGS. 18 to 20.

FIG. 18 shows (part of) a Tanner graph of the parity check matrix of theLDPC code.

If a plurality of (code bits corresponding to) variable nodes connectingto a check node such as two variable nodes suffer from an error such aserasure at the same time as shown in FIG. 18, then the check nodereturns a message of an equal probability representing that theprobability that the value may be 0 and the probability that the valuemay be 1 are equal to each other to all variable nodes connecting to thecheck node. Therefore, if a plurality of variable nodes connecting tothe same check node are placed into an erasure state or the like at thesame time, then the performance in decoding is deteriorated.

Incidentally, an LDPC code outputted from the LDPC encoding section 21of FIG. 8 and prescribed in the DVB-S.2 standard is an IRA code, and theparity matrix H_(T) of the parity check matrix H has a staircasestructure as shown in FIG. 10.

FIG. 19 illustrates a parity matrix H_(T) having a staircase structureand a Tanner graph corresponding to the parity matrix H_(T).

In particular, FIG. 19A illustrates a parity matrix H_(T) having astaircase structure and FIG. 19B shows a Tanner graph corresponding tothe parity matrix H_(T) of FIG. 19A.

Where the parity matrix H_(T) has a staircase structure, in the Tannergraph of the parity matrix H_(T), variable nodes of the LDPC code whichcorrespond to a column of an element of the parity matrix H_(T) havingthe value of 1 and whose message is determined using adjacent code bits(parity bits) are connected to the same check node.

Accordingly, if the adjacent parity bits described above are placed intoan error state by burst errors, erasure or the like, then since a checknode connecting to a plurality of variable nodes corresponding to theplural parity bits which have become an error (variable nodes whosemessage are to be determined using parity bits) returns a message of anequal probability representing that the probability that the value maybe 0 and the probability that the value is 1 may be equal to each otherto the variable nodes connecting to the check node, the performance ofthe decoding deteriorates. Then, where the burst length (number of bitswhich are made an error by a burst) is great, the performance of thedecoding further deteriorates.

Therefore, in order to prevent the deterioration in performance ofdecoding described above, the parity interleaver 23 (FIG. 8) carries outinterleave of interleaving parity bits of the LDPC code from the LDPCencoding section 21 to positions of other parity bits.

FIG. 20 illustrates a parity matrix H_(T) of a parity check matrix Hcorresponding to the LDPC code after the parity interleave carried outby the parity interleaver 23 of FIG. 8.

Here, the information matrix H_(A) of the parity check matrix Hcorresponding to the LDPC code prescribed in the DVB-S.2 standard andoutputted from the LDPC encoding section 21 has a cyclic structure.

The cyclic structure signifies a structure wherein a certain columncoincides with another column in a cyclically operated state (rotation)and includes, for example, a structure wherein, for every P columns, thepositions of the value 1 in the rows of the P columns coincide withpositions to which the first one of the P columns is cyclically shiftedin the column direction by a value which increases in proportion to avalue q obtained by dividing the parity length M. In the following, thenumber of P columns in a cyclic structure is hereinafter referred tosuitably as a unit column number of the cyclic structure.

As an LDPC code prescribed in the DVB-S.2 standard and outputted fromthe LDPC encoding section 21, two LDPC codes are available includingthose whose code length N is 64,800 bits and 16,200 bits as describedhereinabove with reference to FIG. 11.

Now, if attention is paid to the LDPC code whose code length N is 64,800bits from the two different LDPC codes whose code length N is 64,800bits and 16,200 bits, then eleven different encoding rates are availableas the encoding rate of the LDPC code whose code length N is 64,800 bitsas described hereinabove with reference to FIG. 11.

With regard to LDPC codes whose code length N is 64,800 bits and whichhave the eleven different encoding rates, it is prescribed in theDVB-S.2 standard that the column number P of the cyclic structure isprescribed to 360 which is one of divisors of the parity length M except1 and M.

Further, with regard to LDPC codes whose code length N is 64,800 bitsand which have the eleven different encoding rates, the parity length Mhas a value other than prime numbers and represented by an expressionM=q×P=q×360 using the value q which is different depending upon theencoding rate. Accordingly, also the value q is one of the divisors ofthe parity length M except 1 and M similarly to the column number P ofthe cyclic structure and is obtained by dividing the parity length M bythe column number P of the cyclic structure (the product of P and qwhich are divisors of the parity length M is the parity length M).

Where the information length is represented by K and an integer higherthan 0 but lower than P is represented by x while an integer higher than0 but lower than q is represented by y, the parity interleaver 23interleaves, as parity interleave, the K+qx+y+1th code bit from amongparity bits which are K+1th to K+Mth (K+M=N) bits of the LDPC code fromthe LDPC encoding section 21 to the position of the K+Py+x+1th code bit.

According to such parity interleave, since the (parity bitscorresponding to) variable nodes connecting to the same check node arespaced by a distance corresponding to the column number P of the cyclicstructure, here, by 360 bits, where the burst length is smaller than 360bits, such a situation that a plurality of variable nodes connecting tothe same check node are rendered erroneous at the same time can beprevented. As a result, the tolerance to a burst error can be improved.

It is to be noted that the LDPC code after the parity interleave bywhich the K+qx+y+1th code bit is interleaved to the position of theK+Py+x+1th code bit coincides with the LDPC code of a parity checkmatrix (hereinafter referred to also as conversion parity check matrix)obtained by column replacement of replacing the K+qx+y+1th column of theoriginal parity check matrix H into the K+Py+x+1th column.

Further, in the parity matrix of the conversion parity check matrix, apseudo cyclic structure whose unit is P columns (in FIG. 20, 360columns) appears as seen in FIG. 20.

Here, the pseudo cyclic structure signifies a structure which has aportion having a cyclic structure except part thereof. In a conversionparity check column obtained by applying column replacementcorresponding to parity interleave to the parity check matrix of theLDPC code prescribed in the DVB-S.2 standard, a portion of 360 rows×360columns (shift matrix hereinafter described) at a right corner portionis short of one element of 1 (which has the value of 0). Therefore, theconversion parity check matrix does not have a (complete) cyclicstructure but has a pseudo cyclic structure.

It is to be noted that the conversion parity check matrix of FIG. 20 isa matrix to which also replacement of rows (row replacement) forconfiguring the conversion parity check matrix from a configurationmatrix hereinafter described is applied to the original parity checkmatrix H in addition to the column replacement which corresponds toparity interleave.

Now, column twist interleave as a re-arrangement process by the columntwist interleaver 24 of FIG. 8 is described with reference to FIGS. 21to 24.

In the transmission apparatus 11 of FIG. 8, two or more of the code bitsof the LDPC code are transmitted as one symbol as described hereinabovein order to improve the utilization efficiency of frequencies. Inparticular, for example, where 2 bits of the code bits are used to formone symbol, for example, QPSK is used as the modulation method, butwhere 4 bits of the code bits are used to form one symbol, for example,16QAM is used as the modulation method.

Where two or more ones of the code bits are transmitted as one symbol inthis manner, if erasure or the like occurs with a certain symbol, theall of the code bits (allocated to the symbol bits) of the symbol becomean error (erasure).

Accordingly, in order to lower the probability that a plurality of (codebits corresponding to) variable nodes connecting to the same check nodemay suffer from erasure at the same time to improve the performance indecoding, it is necessary to avoid the variable nodes corresponding tocode bits of one symbol from connecting to the same check node.

Meanwhile, in the parity check matrix H of an LDPC code prescribed inthe DVB-S.2 standard and outputted from the LDPC encoding section 21,the information matrix H_(A) has a cyclic structure and the paritymatrix H_(T) has a staircase structure as described hereinabove. Then,in a conversion parity check matrix which is a parity check matrix ofthe LDPC code after parity interleave, a cyclic structure (accurately, apseudo cyclic structure as described hereinabove) appears also in theparity matrix as described in FIG. 20.

FIG. 21 shows a conversion parity check matrix.

In particular, FIG. 21A illustrates a conversion parity check matrix ofa parity check matrix H which has a code length N of 64,800 bits and anencoding rate (r) of 3/4.

In FIG. 21A, the position of an element having the value of 1 in theconversion parity check matrix is indicated by a dot (•).

In FIG. 21B, a process carried out by the demultiplexer 25 (FIG. 8) forthe LDPC code of the conversion parity check matrix of FIG. 21A, thatis, the LDPC code after the parity interleave.

In FIG. 21B, the code bits of the LDPC code after the parity interleaveare written in the column direction in four columns which form thememory 31 of the demultiplexer 25 using 16QAM as the modulation method.

The code bits written in the column direction in the four columns whichform the memory 31 are read out in the row direction in a unit of 4 bitswhich make one symbol.

In this instance, the 4 code bits B₀, B₁, B₂ and B₃ which make onesymbol sometimes make code bits corresponding to 1 and included in onearbitrary row of the parity check matrix after the conversion of FIG.21A, and in this instance, variable nodes corresponding to the code bitsB₀, B₁, B₂ and B₃ are connected to the same check node.

Accordingly, where the 4 code bits B₀, B₁, B₂ and B₃ of one symbolbecome code bits corresponding to 1 and included in one arbitrary row ofthe conversion parity check matrix, if erasure occurs with the symbol,then the same check node to which the variable nodes corresponding tothe code bits B₀, B₁, B₂ and B₃ are connected cannot determine anappropriate message. As a result, the performance in decodingdeteriorates.

Also with regard to the encoding rates other than the encoding rate of3/4, a plurality of code bits corresponding to a plurality of variablenodes connecting to the same check node sometimes make one symbol of16QAM similarly.

Therefore, the column twist interleaver 24 carries out column twistinterleave wherein the code bits of the LDPC code after the parityinterleave from the parity interleaver 23 are interleaved such that aplurality of code bits corresponding to 1 and included in one arbitraryrow of the conversion parity check matrix are not included to onesymbol.

FIG. 22 is a view illustrating the column twist interleave.

In particular, FIG. 22 illustrates the memory 31 (FIGS. 16 and 17) ofthe demultiplexer 25.

The memory 31 has a storage capacity for storing mb bits in the column(vertical) direction and stores N/(mb) bits in the row (horizontal)direction and includes mb columns as described in FIG. 16. Then, thecolumn twist interleaver 24 writes the code bits of the LDPC code in thecolumn direction into the memory 31 and controls the writing startingposition when the code bits are read out in the row direction to carryout column twist interleave.

In particular, the column twist interleaver 24 suitably changes thewriting starting position at which writing of code bits is to be startedfor each of a plurality of columns so that a plurality of code bits readout in the row direction and used to make one symbol may not become codebits corresponding to 1 and included in one arbitrary row of theconversion parity check matrix (re-arranges the code bits of the LDPCcode such that a plurality of code bits corresponding to 1 and includedin one arbitrary row of the parity check matrix may not be included inthe same symbol).

Here, FIG. 22 shows an example of a configuration of the memory 31 wherethe modulation method is 16QAM and besides the multiple b describedhereinabove with reference to FIG. 16 is 1. Accordingly, the bit numberm of code bits of an LDPC code to be one symbol is 4 bits, and thememory 31 is formed from four (=mb) columns.

The column twist interleaver 24 (instead of the demultiplexer 25 shownin FIG. 16) carries out writing of the code bits of the LDPC code in adownward direction (column direction) from above into the four columnswhich form the memory 31 beginning with a left side column towards aright side column.

Then, when the writing of code bits ends to the rightmost column, thecolumn twist interleaver 24 reads out the code bits in a unit of 4 bits(mb bits) in the row direction beginning with the first row of allcolumns which form the memory 31 and outputs the code bits as an LDPCcode after the column twist interleave to the replacement section 32(FIGS. 16 and 17) of the demultiplexer 25.

However, if the address of the head (uppermost) position of each columnis represented by 0 and the addresses of the positions in the columndirection are represented by integers of an ascending order, then thecolumn twist interleaver 24 sets, for the leftmost column, the writingstarting position to the position whose address is 0; sets, for thesecond column (from the left), the writing starting position to theposition whose address is 2; sets, for the third column, the writingstarting position to the position whose address is 4; and sets, for thefourth column, the writing starting position to the position whoseaddress is 7.

It is to be noted that, with regard to the columns for which the writingstarting position is any other position than the position whose addressis 0, after the code bits are written down to the lowermost position,the writing position returns to the top (position whose address is 0)and writing down to a position immediately preceding to the writingstarting position is carried out. Thereafter, writing into the next(right) column is carried out.

By carrying out such column twist interleave as described above, such asituation that a plurality of code bits corresponding to a plurality ofvariable nodes connecting to the same check node are made one symbol of16QAM (included into the same symbol) with regard to LDPC codes of allencoding rates whose code length N is 64,800 as prescribed in theDVB-S.2 standard can be prevented, and as a result, the performance indecoding in a communication path which provides erasure can be improved.

FIG. 23 illustrates the number of columns of the memory 31 necessary forcolumn twist interleave and the address of the writing starting positionfor each modulation method with regard to LDPC codes of the elevendifferent encoding rates having the code length N of 64,800 asprescribed in the DVB-S.2 standard.

Where the multiple b is 1 and besides, since, for example, QPSK isadopted as the modulation method, the bit number m of one symbol is 2bits, according to FIG. 23, the memory 31 has two columns for storing2×1 (=mb) bits in the row direction and stores 64,800/(2×1) bits in thecolumn direction.

Then, the writing starting position for the first one of the two columnsof the memory 31 is set to the position whose address is 0, and thewriting starting position for the second column is set to the positionwhose address is 2.

It is to be noted that the multiple b is 1, for example, where one ofthe first to third replacement methods of FIG. 16 is adopted as thereplacement method of the replacement process of the demultiplexer 25(FIG. 8) or in a like case.

Where the multiple b is 2 and besides, since, for example, QPSK isadopted as the modulation method, the bit number m of one symbol is 2bits, according to FIG. 23, the memory 31 has four columns for storing2×2 bits in the row direction and stores 64,800/(2×2) bits in the columndirection.

Then, the writing starting position for the first one of the fourcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 2, the writing starting position for the third columnis set to the position whose address is 4, and the writing startingposition for the fourth column is set to the position whose address is7.

It is to be noted that the multiple b is 2, for example, where fourthreplacement method of FIG. 17 is adopted as the replacement method ofthe replacement process of the demultiplexer 25 (FIG. 8).

Where the multiple b is 1 and besides, since, for example, 16QAM isadopted as the modulation method, the bit number m of one symbol is 4bits, according to FIG. 23, the memory 31 has four columns for storing4×1 bits in the row direction and stores 64,800/(4×1) bits in the columndirection.

Then, the writing starting position for the first one of the fourcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 2, the writing starting position for the third columnis set to the position whose address is 4, and the writing startingposition for the fourth column is set to the position whose address is7.

Where the multiple b is 2 and besides, since, for example, 16QAM isadopted as the modulation method, the bit number m of one symbol is 4bits, according to FIG. 23, the memory 31 has eight columns for storing4×2 bits in the row direction and stores 64,800/(4×2) bits in the columndirection.

Then, the writing starting position for the first one of the eightcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 2, the writing starting positionfor the fourth column is set to the position whose address is 4, thewriting starting position for the fifth column is set to the positionwhose address is 4, the writing starting position for the sixth columnis set to the position whose address is 5, the writing starting positionfor the seventh column is set to the position whose address is 7, andthe writing starting position for the eighth column is set to theposition whose address is 7.

Where the multiple b is 1 and besides, since, for example, 64QAM isadopted as the modulation method, the bit number m of one symbol is 6bits, according to FIG. 23, the memory 31 has six columns for storing6×1 bits in the row direction and stores 64,800/(6×1) bits in the columndirection.

Then, the writing starting position for the first one of the six columnsof the memory 31 is set to the position whose address is 0, the writingstarting position for the second column is set to the position whoseaddress is 2, the writing starting position for the third column is setto the position whose address is 5, the writing starting position forthe fourth column is set to the position whose address is 9 the writingstarting position for the fifth column is set to the position whoseaddress is 10, and the writing starting position for the sixth column isset to the position whose address is 13.

Where the multiple b is 2 and besides, since, for example, 64QAM isadopted as the modulation method, the bit number m of one symbol is 6bits, according to FIG. 23, the memory 31 has twelve columns for storing6×2 bits in the row direction and stores 64,800/(6×2) bits in the columndirection.

Then, the writing starting position for the first one of the twelvecolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 2, the writing starting positionfor the fourth column is set to the position whose address is 2, thewriting starting position for the fifth column is set to the positionwhose address is 3, the writing starting position for the sixth columnis set to the position whose address is 4, the writing starting positionfor the seventh column is set to the position whose address is 4, thewriting starting position for the eighth column is set to the positionwhose address is 5, the writing starting position for the ninth columnis set to the position whose address is 5, the writing starting positionfor the tenth column is set to the position whose address is 7, thewriting starting position for the eleventh column is set to the positionwhose address is 8, and the writing starting position for the twelfthcolumn is set to the position whose address is 9.

Where the multiple b is 1 and besides, since, for example, 256QAM isadopted as the modulation method, the bit number m of one symbol is 8bits, according to FIG. 23, the memory 31 has eight columns for storing8×1 bits in the row direction and stores 64,800/(8×1) bits in the columndirection.

Then, the writing starting position for the first one of the eightcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 2, the writing starting positionfor the fourth column is set to the position whose address is 4, thewriting starting position for the fifth column is set to the positionwhose address is 4, the writing starting position for the sixth columnis set to the position whose address is 5, the writing starting positionfor the seventh column is set to the position whose address is 7, andthe writing starting position for the eighth column is set to theposition whose address is 7.

Where the multiple b is 2 and besides, since, for example, 256QAM isadopted as the modulation method, the bit number m of one symbol is 8bits, according to FIG. 23, the memory 31 has sixteenth columns forstoring 8×2 bits in the row direction and stores 64,800/(8×2) bits inthe column direction.

Then, the writing starting position for the first one of the sixteencolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 2, the writing starting position for the third columnis set to the position whose address is 2, the writing starting positionfor the fourth column is set to the position whose address is 2, thewriting starting position for the fifth column is set to the positionwhose address is 2, the writing starting position for the sixth columnis set to the position whose address is 3, the writing starting positionfor the seventh column is set to the position whose address is 7, thewriting starting position for the eighth column is set to the positionwhose address is 15, the writing starting position for the ninth columnis set to the position whose address is 16, the writing startingposition for the tenth column is set to the position whose address is20, the writing starting position for the eleventh column is set to theposition whose address is 22, the writing starting position for thetwelfth column is set to the position whose address is 22, the writingstarting position for the thirteenth column is set to the position whoseaddress is 27, the writing starting position for the fourteenth columnis set to the position whose address is 27, the writing startingposition for the fifteenth column is set to the position whose addressis 28, and the writing starting position for the sixteenth column is setto the position whose address is 32.

Where the multiple b is 1 and besides, since, for example, 1024QAM isadopted as the modulation method, the bit number m of one symbol is 10bits, according to FIG. 23, the memory 31 has ten columns for storing10×1 bits in the row direction and stores 64,800/(10×1) bits in thecolumn direction.

Then, the writing starting position for the first one of the ten columnsof the memory 31 is set to the position whose address is 0, the writingstarting position for the second column is set to the position whoseaddress is 3, the writing starting position for the third column is setto the position whose address is 6, the writing starting position forthe fourth column is set to the position whose address is 8, the writingstarting position for the fifth column is set to the position whoseaddress is 11, the writing starting position for the sixth column is setto the position whose address is 13, the writing starting position forthe seventh column is set to the position whose address is 15, thewriting starting position for the eighth column is set to the positionwhose address is 17, the writing starting position for the ninth columnis set to the position whose address is 18, and the writing startingposition for the tenth column is set to the position whose address is20.

Where the multiple b is 2 and besides, since, for example, 1024QAM isadopted as the modulation method, the bit number m of one symbol is 10bits, according to FIG. 23, the memory 31 has twenty columns for storing10×2 bits in the row direction and stores 64,800/(10×2) bits in thecolumn direction.

Then, the writing starting position for the first one of the twentycolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 1, the writing starting position for the third columnis set to the position whose address is 3, the writing starting positionfor the fourth column is set to the position whose address is 4, thewriting starting position for the fifth column is set to the positionwhose address is 5, the writing starting position for the sixth columnis set to the position whose address is 6, the writing starting positionfor the seventh column is set to the position whose address is 6, thewriting starting position for the eighth column is set to the positionwhose address is 9, the writing starting position for the ninth columnis set to the position whose address is 13, the writing startingposition for the tenth column is set to the position whose address is14, the writing starting position for the eleventh column is set to theposition whose address is 14, the writing starting position for thetwelfth column is set to the position whose address is 16, the writingstarting position for the thirteenth column is set to the position whoseaddress is 21, the writing starting position for the fourteenth columnis set to the position whose address is 21, the writing startingposition for the fifteenth column is set to the position whose addressis 23, the writing starting position for the sixteenth column is set tothe position whose address is 25, the writing starting position for theseventeenth column is set to the position whose address is 25, thewriting starting position for the eighteenth column is set to theposition whose address is 26, the writing starting position for thenineteenth column is set to the position whose address is 28, and thewriting starting position for the twentieth column is set to theposition whose address is 30.

Where the multiple b is 1 and besides, since, for example, 4096QAM isadopted as the modulation method, the bit number m of one symbol is 12bits, according to FIG. 23, the memory 31 has twelve columns for storing12×1 bits in the row direction and stores 64,800/(12×1) bits in thecolumn direction.

Then, the writing starting position for the first one of the twelvecolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 2, the writing starting positionfor the fourth column is set to the position whose address is 2, thewriting starting position for the fifth column is set to the positionwhose address is 3, the writing starting position for the sixth columnis set to the position whose address is 4, the writing starting positionfor the seventh column is set to the position whose address is 4, thewriting starting position for the eighth column is set to the positionwhose address is 5, the writing starting position for the ninth columnis set to the position whose address is 5, the writing starting positionfor the tenth column is set to the position whose address is 7, thewriting starting position for the eleventh column is set to the positionwhose address is 8, and the writing starting position for the twelfthcolumn is set to the position whose address is 9.

Where the multiple b is 2 and besides, since, for example, 4096QAM isadopted as the modulation method, the bit number m of one symbol is 12bits, according to FIG. 23, the memory 31 has twenty-four columns forstoring 12×2 bits in the row direction and stores 64,800/(12×2) bits inthe column direction.

Then, the writing starting position for the first one of the twenty-fourcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 5, the writing starting position for the third columnis set to the position whose address is 8, the writing starting positionfor the fourth column is set to the position whose address is 8, thewriting starting position for the fifth column is set to the positionwhose address is 8, the writing starting position for the sixth columnis set to the position whose address is 8, the writing starting positionfor the seventh column is set to the position whose address is 10, thewriting starting position for the eighth column is set to the positionwhose address is 10, the writing starting position for the ninth columnis set to the position whose address is 10, the writing startingposition for the tenth column is set to the position whose address is12, the writing starting position for the eleventh column is set to theposition whose address is 13, the writing starting position for thetwelfth column is set to the position whose address is 16, the writingstarting position for the thirteenth column is set to the position whoseaddress is 17, the writing starting position for the fourteenth columnis set to the position whose address is 19, the writing startingposition for the fifteenth column is set to the position whose addressis 21, the writing starting position for the sixteenth column is set tothe position whose address is 22, the writing starting position for theseventeenth column is set to the position whose address is 23, thewriting starting position for the eighteenth column is set to theposition whose address is 26, the writing starting position for thenineteenth column is set to the position whose address is 37, thewriting starting position for the twentieth column is set to theposition whose address is 39, the writing starting position for thetwenty-first column is set to the position whose address is 40, thewriting starting position for the twenty-second column is set to theposition whose address is 41, the writing starting position for thetwenty-third column is set to the position whose address is 41, and thewriting starting position for the twenty-fourth column is set to theposition whose address is 41.

FIG. 24 indicates the number of columns of the memory 31 necessary forcolumn twist interleave and the address of the writing starting positionfor each modulation method with regard to the LDPC codes of the 10different encoding rates having the code length N of 16,200 asprescribed in the DVB-S.2 standard.

Where the multiple b is 1 and besides, since, for example, QPSK isadopted as the modulation method, the bit number m of one symbol is 2bits, according to FIG. 24, the memory 31 has two columns for storing2×1 bits in the row direction and stores 16,200/(2×1) bits in the columndirection.

Then, the writing starting position for the first one of the two columnsof the memory 31 is set to the position whose address is 0, and thewriting starting position for the second column is set to the positionwhose address is 0.

Where the multiple b is 2 and besides, since, for example, QPSK isadopted as the modulation method, the bit number m of one symbol is 2bits, according to FIG. 24, the memory 31 has four columns for storing2×2 bits in the row direction and stores 16,200/(2×2) bits in the columndirection.

Then, the writing starting position for the first one of the fourcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 2, the writing starting position for the third columnis set to the position whose address is 3, and the writing startingposition for the fourth column is set to the position whose address is3.

Where the multiple b is 1 and besides, since, for example, 16QAM isadopted as the modulation method, the bit number m of one symbol is 4bits, according to FIG. 24, the memory 31 has four columns for storing4×1 bits in the row direction and stores 16,200/(4×1) bits in the columndirection.

Then, the writing starting position for the first one of the fourcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 2, the writing starting position for the third columnis set to the position whose address is 3, and the writing startingposition for the fourth column is set to the position whose address is3.

Where the multiple b is 2 and besides, since, for example, 16QAM isadopted as the modulation method, the bit number m of one symbol is 4bits, according to FIG. 24, the memory 31 has eight columns for storing4×2 bits in the row direction and stores 16,200/(4×2) bits in the columndirection.

Then, the writing starting position for the first one of the eightcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 0, the writing starting positionfor the fourth column is set to the position whose address is 1, thewriting starting position for the fifth column is set to the positionwhose address is 7, the writing starting position for the sixth columnis set to the position whose address is 20, the writing startingposition for the seventh column is set to the position whose address is20, and the writing starting position for the eighth column is set tothe position whose address is 21.

Where the multiple b is 1 and besides, since, for example, 64QAM isadopted as the modulation method, the bit number m of one symbol is 6bits, according to FIG. 24, the memory 31 has six columns for storing6×1 bits in the row direction and stores 16,200/(6×1) bits in the columndirection.

Then, the writing starting position for the first one of the six columnsof the memory 31 is set to the position whose address is 0, the writingstarting position for the second column is set to the position whoseaddress is 0, the writing starting position for the third column is setto the position whose address is 2, the writing starting position forthe fourth column is set to the position whose address is 3 the writingstarting position for the fifth column is set to the position whoseaddress is 7, and the writing starting position for the sixth column isset to the position whose address is 7.

Where the multiple b is 2 and besides, since, for example, 64QAM isadopted as the modulation method, the bit number m of one symbol is 6bits, according to FIG. 24, the memory 31 has twelve columns for storing6×2 bits in the row direction and stores 16,200/(6×2) bits in the columndirection.

Then, the writing starting position for the first one of the twelvecolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 0, the writing starting positionfor the fourth column is set to the position whose address is 2, thewriting starting position for the fifth column is set to the positionwhose address is 2, the writing starting position for the sixth columnis set to the position whose address is 2, the writing starting positionfor the seventh column is set to the position whose address is 3, thewriting starting position for the eighth column is set to the positionwhose address is 3, the writing starting position for the ninth columnis set to the position whose address is 3, the writing starting positionfor the tenth column is set to the position whose address is 6, thewriting starting position for the eleventh column is set to the positionwhose address is 7, and the writing starting position for the twelfthcolumn is set to the position whose address is 7.

Where the multiple b is 1 and besides, since, for example, 256QAM isadopted as the modulation method, the bit number m of one symbol is 8bits, according to FIG. 24, the memory 31 has eight columns for storing8×1 bits in the row direction and stores 16,200/(8×1) bits in the columndirection.

Then, the writing starting position for the first one of the eightcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 0, the writing starting positionfor the fourth column is set to the position whose address is 1, thewriting starting position for the fifth column is set to the positionwhose address is 7, the writing starting position for the sixth columnis set to the position whose address is 20, the writing startingposition for the seventh column is set to the position whose address is20, and the writing starting position for the eighth column is set tothe position whose address is 21.

Where the multiple b is 1 and besides, since, for example, 1024QAM isadopted as the modulation method, the bit number m of one symbol is 10bits, according to FIG. 24, the memory 31 has ten columns for storing10×1 bits in the row direction and stores 16,200/(10×1) bits in thecolumn direction.

Then, the writing starting position for the first one of the ten columnsof the memory 31 is set to the position whose address is 0, the writingstarting position for the second column is set to the position whoseaddress is 1, the writing starting position for the third column is setto the position whose address is 2, the writing starting position forthe fourth column is set to the position whose address is 2, the writingstarting position for the fifth column is set to the position whoseaddress is 3, the writing starting position for the sixth column is setto the position whose address is 3, the writing starting position forthe seventh column is set to the position whose address is 4, thewriting starting position for the eighth column is set to the positionwhose address is 4, the writing starting position for the ninth columnis set to the position whose address is 5, and the writing startingposition for the tenth column is set to the position whose address is 7.

Where the multiple b is 2 and besides, since, for example, 1024QAM isadopted as the modulation method, the bit number m of one symbol is 10bits, according to FIG. 24, the memory 31 has twenty columns for storing10×2 bits in the row direction and stores 16,200/(10×2) bits in thecolumn direction.

Then, the writing starting position for the first one of the twentycolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 0, the writing starting positionfor the fourth column is set to the position whose address is 2, thewriting starting position for the fifth column is set to the positionwhose address is 2, the writing starting position for the sixth columnis set to the position whose address is 2, the writing starting positionfor the seventh column is set to the position whose address is 2, thewriting starting position for the eighth column is set to the positionwhose address is 2, the writing starting position for the ninth columnis set to the position whose address is 5, the writing starting positionfor the tenth column is set to the position whose address is 5, thewriting starting position for the eleventh column is set to the positionwhose address is 5, the writing starting position for the twelfth columnis set to the position whose address is 5, the writing starting positionfor the thirteenth column is set to the position whose address is 5, thewriting starting position for the fourteenth column is set to theposition whose address is 7, the writing starting position for thefifteenth column is set to the position whose address is 7, the writingstarting position for the sixteenth column is set to the position whoseaddress is 7, the writing starting position for the seventeenth columnis set to the position whose address is 7, the writing starting positionfor the eighteenth column is set to the position whose address is 8, thewriting starting position for the nineteenth column is set to theposition whose address is 8, and the writing starting position for thetwentieth column is set to the position whose address is 10.

Where the multiple b is 1 and besides, since, for example, 4096QAM isadopted as the modulation method, the bit number m of one symbol is 12bits, according to FIG. 24, the memory 31 has twelve columns for storing12×1 bits in the row direction and stores 16,200/(12×1) bits in thecolumn direction.

Then, the writing starting position for the first one of the twelvecolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 0, the writing starting positionfor the fourth column is set to the position whose address is 2, thewriting starting position for the fifth column is set to the positionwhose address is 2, the writing starting position for the sixth columnis set to the position whose address is 2, the writing starting positionfor the seventh column is set to the position whose address is 3, thewriting starting position for the eighth column is set to the positionwhose address is 3, the writing starting position for the ninth columnis set to the position whose address is 3, the writing starting positionfor the tenth column is set to the position whose address is 6, thewriting starting position for the eleventh column is set to the positionwhose address is 7, and the writing starting position for the twelfthcolumn is set to the position whose address is 7.

Where the multiple b is 2 and besides, since, for example, 4096QAM isadopted as the modulation method, the bit number m of one symbol is 12bits, according to FIG. 24, the memory 31 has twenty-four columns forstoring 12×2 bits in the row direction and stores 16,200/(12×2) bits inthe column direction.

Then, the writing starting position for the first one of the twenty-fourcolumns of the memory 31 is set to the position whose address is 0, thewriting starting position for the second column is set to the positionwhose address is 0, the writing starting position for the third columnis set to the position whose address is 0, the writing starting positionfor the fourth column is set to the position whose address is 0, thewriting starting position for the fifth column is set to the positionwhose address is 0, the writing starting position for the sixth columnis set to the position whose address is 0, the writing starting positionfor the seventh column is set to the position whose address is 0, thewriting starting position for the eighth column is set to the positionwhose address is 1, the writing starting position for the ninth columnis set to the position whose address is 1, the writing starting positionfor the tenth column is set to the position whose address is 1, thewriting starting position for the eleventh column is set to the positionwhose address is 2, the writing starting position for the twelfth columnis set to the position whose address is 2, the writing starting positionfor the thirteenth column is set to the position whose address is 2, thewriting starting position for the fourteenth column is set to theposition whose address is 3, the writing starting position for thefifteenth column is set to the position whose address is 7, the writingstarting position for the sixteenth column is set to the position whoseaddress is 9, the writing starting position for the seventeenth columnis set to the position whose address is 9, the writing starting positionfor the eighteenth column is set to the position whose address is 9, thewriting starting position for the nineteenth column is set to theposition whose address is 10, the writing starting position for thetwentieth column is set to the position whose address is 10, the writingstarting position for the twenty-first column is set to the positionwhose address is 10, the writing starting position for the twenty-secondcolumn is set to the position whose address is 10, the writing startingposition for the twenty-third column is set to the position whoseaddress is 10, and the writing starting position for the twenty-fourthcolumn is set to the position whose address is 11.

Now, a transmission process carried out by the transmission apparatus 11of FIG. 8 is described with reference to a flow chart of FIG. 25.

The LDPC encoding section 21 waits that object data are supplied theretoand, at step S101, encodes the object data into LDPC codes and suppliesthe LDCP codes to the bit interleaver 22. Thereafter, the processingadvances to step S102.

At step S102, the bit interleaver 22 carries out bit interleave for theLDPC codes from the LDPC encoding section 21 and supplies to the mappingsection 26 a symbol in which the LDPC codes after the interleave aresymbolized. Thereafter, the processing advances to step S103.

In particular, at step S102, the parity interleaver 23 in the bitinterleaver 22 carries out parity interleave for the LDPC codes from theLDPC encoding section 21 and supplies the LDPC codes after the parityinterleave to the column twist interleaver 24.

The column twist interleaver 24 carries out column twist interleave forthe LDPC code from the parity interleaver 23 and supplies a result ofthe column twist interleave to the demultiplexer 25.

The demultiplexer 25 carries out a replacement process of replacing thecode bits of the LDPC code after the column twist interleave by thecolumn twist interleaver 24 and converting the code bits after thereplacement into symbol bits (bits representative of symbols) ofsymbols.

Here, the replacement process by the demultiplexer 25 can be carried outin accordance with the first to fourth replacement methods describedhereinabove with reference to FIGS. 16 and 17 and besides can be carriedout in accordance with an allocation rule. The allocation rule is a rulefor allocating code bits of an LDPC code to symbol bits representativeof symbols, and details of the allocation rule are hereinafterdescribed.

The symbols obtained by the replacement process by the demultiplexer 25are supplied from the demultiplexer 25 to the mapping section 26.

At step S103, the mapping section 26 maps the symbol from thedemultiplexer 25 to signal points defined by the modulation method oforthogonal modulation carried out by the orthogonal modulation section27 and supplies the mapped symbol to the orthogonal modulation section27. Then, the processing advances to step S104.

At step S104, the orthogonal modulation section 27 carries outorthogonal modulation of a carrier in accordance with the signal pointsfrom the mapping section 26. Then, the processing advances to step S105,at which the modulation signal obtained as a result of the orthogonalmodulation is transmitted, whereafter the processing is ended.

It is to be noted that the transmission process of FIG. 25 is carriedout by pipeline repetitively.

By carrying out the parity interleave and the column twist interleave asdescribed above, the tolerance to erasure or burst errors where aplurality of code bits of an LDPC codes are transmitted as one symbolcan be improved.

Here, while, in FIG. 8, the parity interleaver 23 which is a block forcarrying out parity interleave and the column twist interleaver 24 whichis a block for carrying out column twist interleave are configuredseparately from each other for the convenience of description, theparity interleaver 23 and the column twist interleaver 24 may otherwisebe configured integrally with each other.

In particular, both of the parity interleave and the column twistinterleave can be carried out by writing and reading out of code bitsinto and from a memory and can be represented by a matrix for convertingaddresses (write addresses) into which writing of code bits is to becarried out into addresses (readout addresses) from which reading out ofcode bits is to be carried out.

Accordingly, if a matrix obtained by multiplying a matrix representativeof the parity interleave and a matrix representative of the column twistinterleave is determined in advance, then if the matrix is used toconvert code bits, then a result when parity interleave is carried outand then LDPC codes after the parity interleave are column twistinterleaved can be obtained.

Further, in addition to the parity interleaver 23 and the column twistinterleaver 24, also the demultiplexer 25 may be configured integrally.

In particular, also the replacement process carried out by thedemultiplexer 25 can be represented by a matrix for converting a writeaddress of the memory 31 for storing an LDPC code into a read address.

Accordingly, if a matrix obtained by multiplication of a matrixrepresentative of the parity interleave, another matrix representativeof the column twist interleave and a further matrix representative ofthe replacement process is determined in advance, then the parityinterleave, column twist interleave and replacement process can becarried out collectively by the determined matrix.

It is to be noted that it is possible to carry out only one of or no oneof the parity interleave and the column twist interleave.

Now, a simulation carried out with regard to the transmission apparatus11 of FIG. 8 for measuring the error rate (bit error rate) is describedwith reference to FIGS. 26 to 28.

The simulation was carried out adopting a communication path which has aflutter whose D/U is 0 dB.

FIG. 26 shows a model of the communication path adopted in thesimulation.

In particular, FIG. 26A shows a model of the flutter adopted in thesimulation.

Meanwhile, FIG. 26B shows a model of a communication path which has theflutter represented by the model of FIG. 26A.

It is to be noted that, in FIG. 26B, H represents the model of theflutter of FIG. 26A. Further, in FIG. 26B, N represents ICI (InterCarrier Interference), and in the simulation, an expected value E[N²] ofthe power was approximated by AWGN.

FIGS. 27 and 28 illustrate relationships between the error rate obtainedby the simulation and the Doppler frequency f_(d) of the flutter.

It is to be noted that FIG. 27 illustrates a relationship between theerror rate and the Doppler frequency f_(d) where the modulation methodis 16QAM and the encoding rate (r) is (3/4) and besides the replacementmethod is the first replacement method. Meanwhile, FIG. 28 illustratesthe relationship between the error rate and the Doppler frequency f_(d)where the modulation method is 64QAM and the encoding rate (r) is (5/6)and besides the replacement method is the first replacement method.

Further, in FIGS. 27 and 28, a thick line curve indicates therelationship between the error rate and the Doppler frequency f_(d)where all of the parity interleave, column twist interleave andreplacement process were carried out, and a thin line curve indicatesthe relationship between the error rate and the Doppler frequency f_(d)where only the replacement process from among the parity interleave,column twist interleave and replacement process was carried out.

In both of FIGS. 27 and 28, it can be recognized that the error rateimproves (decreases) where all of the parity interleave, column twistinterleave and replacement process are carried out rather than whereonly the replacement process is carried out.

Now, the LDPC encoding section 21 of FIG. 8 is described furthermore.

As described referring to FIG. 11, in the DVB-S.2 standard, LDPCencoding of the two different code lengths N of 64,800 bits and 16,200bits are prescribed.

And, for the LDPC code whose code length N is 64,800 bits, the 11encoding rates 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9 and 9/10are prescribed, and for the LDPC code whose code length N is 16,200bits, the encoding rates 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6 and8/9 are prescribed (FIG. 11B).

The LDPC encoding section 21 carries out encoding (error correctionencoding) into LDPC codes of the different encoding rates whose codelength N is 64,800 bits or 16,200 bits in accordance with a parity checkmatrix H prepared for each code length N and for each encoding rate.

FIG. 29 shows an example of a configuration of the LDPC encoding section21 of FIG. 8.

The LDPC encoding section 21 includes an encoding processing block 601and a storage block 602.

The encoding processing block 601 includes an encoding rate settingportion 611, an initial value table reading out portion 612, a paritycheck matrix production portion 613, an information bit reading outportion 614, an encoding parity mathematical operation portion 615, anda control portion 616, and carries out LDPC encoding of object datasupplied to the LDPC encoding section 21 and supplies an LDPC codeobtained as a result of the LDPC encoding to the bit interleaver 22(FIG. 8).

In particular, the encoding rate setting portion 611 sets a code lengthN and an encoding rate for LDPC codes, for example, in response to anoperation of an operator.

The initial value table reading out portion 612 reads out a parity checkmatrix initial value table hereinafter described which corresponds tothe code length N and the encoding rate set by the encoding rate settingportion 611 from the storage block 602.

The parity check matrix production portion 613 places, based on theparity check matrix initial value table read out by the initial valuetable reading out portion 612, elements of the value 1 of an informationmatrix H_(A) corresponding to an information length K (=code lengthN−parity length M) corresponding to the code length N and the encodingrate set by the encoding rate setting portion 611 in a period of 360columns (unit column number P of the cyclic structure) in the columndirection to produce a parity check matrix H, and stores the paritycheck matrix H into the storage block 602.

The information bit reading out portion 614 reads out (extracts)information bits for the information length K from the object datasupplied to the LDPC encoding section 21.

The encoding parity mathematical operation portion 615 reads out theparity check matrix H produced by the parity check matrix productionportion 613 from the storage block 602 and calculates parity bitscorresponding to the information bits read out by the information bitreading out portion 614 in accordance with a predetermined expression toproduce a codeword (LDPC code).

The control portion 616 controls the blocks which compose the encodingprocessing block 601.

In the storage block 602, a plurality of parity check matrix initialvalue tables and so forth individually corresponding to the pluralencoding rates illustrated in FIG. 11 in regard to individual ones ofthe two code lengths N of 64,800 bits and 16,200 bits are stored.Further, the storage block 602 temporarily stores data necessary forprocessing of the encoding processing block 601.

FIG. 30 is a flow chart illustrating a reception process carried out bythe reception apparatus 12 of FIG. 29.

At step S201, the encoding rate setting portion 611 determines (sets) acode length N and an encoding rate r used for carrying out LDPCencoding.

At step S202, the initial value table reading out portion 612 reads outfrom the storage block 602 a predetermined parity check matrix initialvalue table corresponding to the code length N and the encoding rate rdetermined by the encoding rate setting portion 611.

At step S203, the parity check matrix production portion 613 determines(produces) a parity check matrix H for an LDPC code having the codelength N and the encoding rate r determined by the encoding rate settingportion 611 using the parity check matrix initial value table read outfrom the storage block 602 by the initial value table reading outportion 612, and supplies the parity check matrix H to the storage block602 so as to be stored.

At step S204, the information bit reading out portion 614 reads outinformation bits of the information length K (=N×r) corresponding to thecode length N and the encoding rate r determined by the encoding ratesetting portion 611 from among the object data supplied to the LDPCencoding section 21 and reads out the parity check matrix H determinedby the parity check matrix production portion 613 from the storage block602, and supplies the information bits and the parity check matrix H tothe encoding parity mathematical operation portion 615.

At step S205, the encoding parity mathematical operation portion 615successively mathematically operates a parity bit of a codeword c whichsatisfies an expression (8).Hc^(T)=0  (8)

In the expression (8), c indicates a row vector as the codeword (LDPCcode), and c^(T) indicates inversion of the row vector c.

Here, as above described, where, from within the row vector c as an LDPCcode (one codeword), a portion corresponding to the information bits isrepresented by a row vector A and a portion corresponding to the paritybits is represented by a row vector T, the row vector c can berepresented by an expression c=[A|T] from the row vector A as theinformation bits and the row vector T as the parity bits.

It is necessary for the parity check matrix H and the row vector c=[A|T]as an LDPC code to satisfy the expression Hc^(T)=0, and where the paritymatrix H_(T) of the parity check matrix H=[H_(A)|H_(T)] has a staircasestructure shown in FIG. 10, the row vector T as parity bits whichconfigures the row vector c=[A|T] which satisfies the expressionHc^(T)=0 can be determined sequentially by setting the elements of eachrow to zero in order beginning with the elements in the first row of thecolumn vector Hc^(T) in the expression Hc^(T)=0.

If the encoding parity mathematical operation portion 615 determines aparity bit T for an information bit A, then it outputs a codewordc=[A|T] represented by the information bit A and the parity bit T as anLDPC encoding result of the information bit A.

It is to be noted that the codeword c has 64,800 bits or 16,200 bits.

Thereafter, at step S206, the control portion 616 decides whether or notthe LDPC encoding should be ended.

If it is decided at step S206 that the LDPC encoding should not beended, that is, for example, if there remain object data to be LDPCencoded, then the processing returns to step S201, and thereafter, theprocesses at steps S201 to S206 are repeated.

On the other hand, if it is decided at step S206 that the LDPC encodingshould be ended, that is, for example, if there remains no object datato be LDPC encoded, the LDPC encoding section 21 ends the processing.

As described above, the parity check matrix initial value tablescorresponding to the code lengths N and the encoding rates r areprepared, and the LDPC encoding section 21 carries out LDPC encoding fora predetermined code length N and a predetermined encoding rate r usinga parity check matrix H produced from a parity check matrix initialvalue table corresponding to the predetermined code length N and thepredetermined encoding rate r.

Each parity check matrix initial value table is a table which representsthe position of elements of the value 1 of the information matrix H_(A)corresponding to the information length K corresponding to the codelength N and the encoding rate r of the LDPC code of the parity checkmatrix H (LDPC code defined by the parity check matrix H) for every 360rows (unit column number P of the periodic structure), and is producedin advance for a parity check matrix H for each code length N and eachencoding rate r.

FIGS. 31 to 58 illustrate some of the parity check matrix initial valuetables prescribed in the DVB-S.2 standard.

In particular, FIG. 31 shows the parity check matrix initial value tablefor a parity check matrix H prescribed in the DVB-S.2 standard andhaving a code length N of 16,200 bits and an encoding rate r of 2/3.

FIGS. 32 to 34 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 2/3.

It is to be noted that FIG. 33 is a view continuing from FIG. 32 andFIG. 34 is a view continuing from FIG. 33.

FIG. 35 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 3/4.

FIGS. 36 to 39 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 3/4.

It is to be noted that FIG. 37 is a view continuing from FIG. 36 andFIG. 38 is a view continuing from FIG. 37. Further, FIG. 39 is a viewcontinuing from FIG. 38.

FIG. 40 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 4/5.

FIGS. 41 to 44 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 4/5.

It is to be noted that FIG. 42 is a view continuing from FIG. 41 andFIG. 43 is a view continuing from FIG. 42. Further, FIG. 44 is a viewcontinuing from FIG. 43.

FIG. 45 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 5/6.

FIGS. 46 to 49 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 5/6.

It is to be noted that FIG. 47 is a view continuing from FIG. 46 andFIG. 48 is a view continuing from FIG. 47. Further, FIG. 49 is a viewcontinuing from FIG. 48.

FIG. 50 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 8/9.

FIGS. 51 to 54 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 8/9.

It is to be noted that FIG. 52 is a view continuing from FIG. 51 andFIG. 53 is a view continuing from FIG. 52. Further, FIG. 54 is a viewcontinuing from FIG. 53.

FIGS. 55 to 58 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 9/10.

It is to be noted that FIG. 56 is a view continuing from FIG. 55 andFIG. 57 is a view continuing from FIG. 56. Further, FIG. 58 is a viewcontinuing from FIG. 57.

The parity check matrix production portion 613 (FIG. 29) determines aparity check matrix H in the following manner using the parity checkmatrix initial value tables.

In particular, FIG. 59 illustrates a method for determining a paritycheck matrix H from a parity check matrix initial value table.

It is to be noted that the parity check matrix initial value table ofFIG. 59 indicates the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 16,200 bits and an encoding rate r of 2/3 shown in FIG.31.

As described above, the parity check matrix initial value table is atable which represents the position of elements of the value 1 of ainformation matrix H_(A) (FIG. 9) corresponding to the informationlength K corresponding to the code length N and the encoding rate r ofthe LDPC code for every 360 columns (for every unit column number P ofthe cyclic structure), and in the first row of the parity check matrixinitial value table, a number of row numbers of elements of the value 1in the 1+360×(i−1)th column of the parity check matrix H (row numberswhere the row number of the first row of the parity check matrix H is 0)equal to the number of column weights which the 1+360×(i−1)th columnhas.

Here, since the parity matrix H_(T) (FIG. 9) of the parity check matrixH which corresponds to the parity length M is determined as illustratedin FIG. 19, according to the parity check matrix initial value table,the information matrix H_(A) (FIG. 9) of the parity check matrix Hcorresponding to the information length K is determined.

The row number k+1 of the parity check matrix initial value tablediffers depending upon the information length K.

The information length K and the row number k+1 of the parity checkmatrix initial value table satisfy a relationship given by an expression(9).K=(k+1)×360  (9)

Here, 360 in the expression (9) is the unit column number P of thecyclic structure described referring to FIG. 20.

In the parity check matrix initial value table of FIG. 59, 13 numericalvalues are listed in the first to third rows, and three numerical valuesare listed in the fourth to k+1th (in FIG. 59, 30th) rows.

Accordingly, the number of column weights in the parity check matrix Hdetermined from the parity check matrix initial value table of FIG. 59is 13 in the first to 1+360×(3−1)−1th rows but is 3 in the 1+360×(3−1)thto Kth rows.

The first row of the parity check matrix initial value table of FIG. 59includes 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451,4620 and 2622, and this indicates that, in the first column of theparity check matrix H, the elements in rows of the row numbers of 0,2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620 and2622 have the value 1 (and besides the other elements have the value 0).

Meanwhile, the second row of the parity check matrix initial value tableof FIG. 59 includes 1, 122, 1516, 3448, 2880, 1407, 1847, 3799, 3529,373, 971, 4358 and 3108, and this indicates that, in the 361st(=1+360×(2−1)th) column of the parity check matrix H, the elements inrows of the row numbers of 1, 122, 1546, 3448, 2880, 1407, 1847, 3799,3529, 373, 971, 4358 and 3108 have the value 1.

As given above, the parity check matrix initial value table representsthe position of elements of the value 1 of the information matrix H_(A)of the parity check matrix H for every 360 columns.

Each of the columns of the parity check matrix H other than the1+360×(i−1)th column, that is, each of the columns from 2+360×(i−1)th to360×ith columns, includes elements of the value of 1 obtained bycyclically shifting the elements of the value of 1 of the 1+360×(i−1)thcolumn which depend upon the parity check matrix initial value tableperiodically in the downward direction (in the downward direction of thecolumn) in accordance with the parity length M.

In particular, for example, the 2+360×(i−1)th column is a columnobtained by cyclically shifting the 1+360×(i−1)th column in the downwarddirection by M/360 (=q), and the next 3+360×(i−1)th is a column obtainedby cyclically shifting the 1+360×(i−1)th column in the downwarddirection by 2×M/360 (=2×q) and then cyclically shifting the cyclicallyshifted column (2+360×(i−1)th column) in the downward direction by M/360(=q).

Now, if it is assumed that the numeral value in the jth column (jth fromthe left) in the ith row (ith row from above) of the parity check matrixinitial value table is represented by b_(i,j) and the row number of thejth element of the value 1 in the wth column of the parity check matrixH is represented by H_(w-j), then the row number H_(w-j) of the elementof the value 1 in the wth column which is a column other than the1+360×(i−1)th column of the parity check matrix H can be determined inaccordance with an expression (10).H _(w-j)=mod {h _(i,j)+mod((w−1),P)×q,M}  (10)

Here, mod(x,y) signifies a remainder when x is divided by y.

Meanwhile, P is a unit number of columns of the cyclic structuredescribed hereinabove and is, for example, in the DVB-S.2 standard, asdescribed above, 360. Further, q is a value M/360 obtained by dividingthe parity length M by the unit column number P (=360) of the cyclicstructure.

The parity check matrix production portion 613 (FIG. 29) specifies therow number of the elements of the value 1 in the 1+360×(i−1)th column ofthe parity check matrix H from the parity check matrix initial valuetable.

Further, the parity check matrix production portion 613 (FIG. 29)determines the row number H_(w-j) of the element of the value 1 in thewth column which is a column other than the 1+360×(i−1)th column of theparity check matrix H in accordance with the expression (10) andproduces a parity check matrix H in which the elements of the rownumbers obtained by the foregoing have the value 1.

Incidentally, it is known that the LDPC code having an encoding rate of2/3 prescribed in the DVB-S.2 standard is inferior (higher) in the errorfloor thereof in comparison with the LDPC codes of the other encodingrates.

Here, a phenomenon (error floor phenomenon) that, as the S/N (E_(s)/N₀)becomes higher, the drop of the error rate (BER) becomes duller and theerror rate stops its drop occurs, and the error rate when the drop stopsis an error floor.

If the error floor becomes higher, then generally the tolerance toerrors in the communication path 13 (FIG. 7) drops, and therefore, it isdesirable to take a countermeasure for improving the tolerance toerrors.

As a countermeasure for improving the tolerance to errors, for example,a replacement process which is carried out by the demultiplexer 25 (FIG.8) is available.

In the replacement process, as a replacement method for replacing codebits of an LDPC code, for example, the first to fourth replacementmethods described hereinabove are available. However, it is demanded topropose a method which has a further improved tolerance to errors incomparison with methods proposed already including the first to fourthreplacement methods.

Thus, the demultiplexer 25 (FIG. 8) is configured such that it can carryout a replacement process in accordance with an allocation rule asdescribed hereinabove with reference to FIG. 25.

In the following, before a replacement process in accordance with anallocation rule is described, a replacement process by replacementmethods (hereinafter referred to existing methods) proposed already isdescribed.

A replacement process where it is assumed that the replacement processis carried out in accordance with the existing methods by thedemultiplexer 25 is described with reference to FIGS. 60 and 61.

FIG. 60 shows an example of the replacement process of an existingmethod where the LDPC code is an LDPC code having a code length N of64,800 bits and an encoding rate of 3/5.

In particular, FIG. 60A illustrates an example of the replacement methodof an existing method where the LDPC code is an LDPC code having a codelength N of 64,800 bits and an encoding rate of 3/5 and besides themodulation method is 16QAM and the multiple b is 2.

Where the modulation method is 16QAM, 4 (=m) bits from among the codebits are mapped as one symbol to some of 16 signal points prescribed by16QAM.

Further, where the code length N is 64,800 bits and the multiple b is 2,the memory 31 (FIGS. 16 and 17) of the demultiplexer 25 has eightcolumns for storing 4×2 (=mb) bits in the row direction and stores64,800/(4×2) bits in the column direction.

In the demultiplexer 25, when the code bits of the LDPC code are writtenin the column direction of the memory 31 and writing of the 64,800 codebits (one codeword) ends, the code bits written in the memory 31 areread out in a unit of 4×2 (=mb) bits in the row direction and suppliedto the replacement section 32 (FIGS. 16 and 17).

The replacement section 32 replaces, for example, the 4×2 (=mb) codebits b₀, b₁, b₂, b₃, b₄, b₅, b₅ and b₇ read out from the memory 31 suchthat, as seen in FIG. 60A, the 4×2 (=mb) code bits b₀ to b₇ areallocated to 4×2 (=mb) symbol bits y₀, y₁, y₂, y₃, y₄, y₅, y₆ and y₇ ofsuccessive two (=b) symbols.

In particular, the replacement section 32 carries out replacement forallocating

the code bit b₀ to the symbol bit y₇,

the code bit b₁ to the symbol bit y₁,

the code bit b₂ to the symbol bit y₄,

the code bit b₃ to the symbol bit y₂,

the code bit b₄ to the symbol bit y₅,

the code bit b₅ to the symbol bit y₃,

the code bit b₅ to the symbol bit y₆, and

the code bit b₇ to the symbol bit y₀.

In particular, FIG. 60B illustrates an example of the replacement methodof an existing method where the LDPC code is an LDPC code having a codelength N of 64,800 bits and an encoding rate of 3/5 and besides themodulation method is 64QAM and the multiple b is 2.

Where the modulation method is 64QAM, 6 (=m) bits from among the codebits are mapped as one symbol to some of 64 signal points prescribed by64QAM.

Further, where the code length N is 64,800 bits and the multiple b is 2,the memory 31 (FIGS. 16 and 17) of the demultiplexer 25 has 12 columnsfor storing 6×2 (=mb) bits in the row direction and stores 64,800/(6×2)bits in the column direction.

In the demultiplexer 25, when the code bits of the LDPC code are writtenin the column direction of the memory 31 and writing of the 64,800 codebits (one codeword) ends, the code bits written in the memory 31 areread out in a unit of 6×2 (=mb) bits in the row direction and suppliedto the replacement section 32 (FIGS. 16 and 17).

The replacement section 32 replaces, for example, the 6×2 (=mb) codebits b₀, b₁, b₂, b₃, b₄, b₅, b₆, b₇, b₈, b₉, b₁₀ and b₁₁ read out fromthe memory 31 such that, as seen in FIG. 60B, the 6×2 (=mb) code bits b₀to b₁₁ are allocated to 6×2 (=mb) symbol bits y₀, y₁, y₂, y₃, y₄, y₅,y₆, y₇, y₈, y₉, y₁₀ and y₁₁ of successive two (=b) symbols.

In particular, the replacement section 32 carries out replacement forallocating

the code bit b₀ to the symbol bit y₁₁,

the code bit b₁ to the symbol bit y₇,

the code bit b₂ to the symbol bit y₃,

the code bit b₃ to the symbol bit y₁₀,

the code bit b₄ to the symbol bit y₆,

the code bit b₅ to the symbol bit y₂,

the code bit b₆ to the symbol bit y₉,

the code bit b₇ to the symbol bit y₅,

the code bit b₈ to the symbol bit y₁,

the code bit b₉ to the symbol bit y₈,

the code bit b₁₀ to the symbol bit y₄, and

the code bit b₁₁ to the symbol bit y₀.

In particular, FIG. 60C illustrates an example of the replacement methodof an existing method where the LDPC code is an LDPC code having a codelength N of 64,800 bits and an encoding rate of 3/5 and besides themodulation method is 256QAM and the multiple b is 2.

Where the modulation method is 256QAM, 8 (=m) bits from among the codebits are mapped as one symbol to some of 256 signal points prescribed by256QAM.

Further, where the code length N is 64,800 bits and the multiple b is 2,the memory 31 (FIGS. 16 and 17) of the demultiplexer 25 has 16 columnsfor storing 8×2 (=mb) bits in the row direction and stores 64,800/(8×2)bits in the column direction.

In the demultiplexer 25, when the code bits of the LDPC code are writtenin the column direction of the memory 31 and writing of the 64,800 codebits (one codeword) ends, the code bits written in the memory 31 areread out in a unit of 8×2 (=mb) bits in the row direction and suppliedto the replacement section 32 (FIGS. 16 and 17).

The replacement section 32 replaces, for example, the 8×2 (=mb) codebits b₀, b₁, b₂, b₃, b₄, b₅, b₆, b₇, b₈, b₉, b₁₀, b₁₁, b₁₂, b₁₃, b₁₄ andb₁₅ read out from the memory 31 such that, as seen in FIG. 60C, the 8×2(=mb) code bits b₀ to b₁₅ are allocated to 8×2 (=mb) symbol bits y₀, y₁,y₂, y₃, y₄, y₅, y₆, y₇, y₈, y₉, y₁₀, y₁₁, y₁₂, y₁₃, y₁₄ and y₁₅ ofsuccessive two (=b) symbols.

In particular, the replacement section 32 carries out replacement forallocating

the code bit b₀ to the symbol bit y₁₅,

the code bit b₁ to the symbol bit y₁,

the code bit b₂ to the symbol bit y₁₃,

the code bit b₃ to the symbol bit y₂,

the code bit b₄ to the symbol bit y₈,

the code bit b₅ to the symbol bit y₁₁,

the code bit b₆ to the symbol bit y₉,

the code bit b₇ to the symbol bit y₅,

the code bit b₈ to the symbol bit y₁₀,

the code bit b₉ to the symbol bit y₆,

the code bit b₁₀ to the symbol bit y₄,

the code bit b₁₁ to the symbol bit y₇,

the code bit b₁₂ to the symbol bit y₁₂,

the code bit b₁₃ to the symbol bit y₂,

the code bit b₁₄ to the symbol bit y₁₄, and

the code bit b₁₅ to the symbol bit y₀.

FIG. 61 shows an example of the replacement process of an existingmethod where the LDPC code is an LDPC code having a code length N of16,200 bits and an encoding rate of 3/5.

In particular, FIG. 61A illustrates an example of the replacement methodof an existing method where the LDPC code is an LDPC code having a codelength N of 16,200 bits and an encoding rate of 3/5 and besides themodulation method is 16QAM and the multiple b is 2.

Where the modulation method is 16QAM, 4 (=m) bits from among the codebits are mapped as one symbol to some of 16 signal points prescribed by16QAM.

Further, where the code length N is 16,200 bits and the multiple b is 2,the memory 31 (FIGS. 16 and 17) of the demultiplexer 25 has 8 columnsfor storing 4×2 (=mb) bits in the row direction and stores 16,200/(4×2)bits in the column direction.

In the demultiplexer 25, when the code bits of the LDPC code are writtenin the column direction of the memory 31 and writing of the 16,200 codebits (one codeword) ends, the code bits written in the memory 31 areread out in a unit of 4×2 (=mb) bits in the row direction and suppliedto the replacement section 32 (FIGS. 16 and 17).

The replacement section 32 replaces, for example, the 4×2 (=mb) codebits b₀, b₁, b₂, b₃, b₄, b₅, b₆ and b₇ read out from the memory 31 suchthat, as seen in FIG. 61A, the 4×2 (=mb) code bits b₀ to b₇ areallocated to 4×2 (=mb) symbol bits y₀, y₁, y₂, y₃, y₄, y₅, y₆ and y₇ ofsuccessive two (=b) symbols.

In particular, the replacement section 32 carries out replacement forallocating the code bits b₀ to b₇ to the symbol bits y₀ to y₇ as in thecase of FIG. 60A described above.

In particular, FIG. 61B illustrates an example of the replacement methodof an existing method where the LDPC code is an LDPC code having a codelength N of 16,200 bits and an encoding rate of 3/5 and besides themodulation method is 64QAM and the multiple b is 2.

Where the modulation method is 64QAM, 6 (=m) bits from among the codebits are mapped as one symbol to some of 64 signal points prescribed by64QAM.

Further, where the code length N is 16,200 bits and the multiple b is 2,the memory 31 (FIGS. 16 and 17) of the demultiplexer 25 has 12 columnsfor storing 6×2 (=mb) bits in the row direction and stores 16,200/(6×2)bits in the column direction.

In the demultiplexer 25, when the code bits of the LDPC code are writtenin the column direction of the memory 31 and writing of the 16,200 codebits (one codeword) ends, the code bits written in the memory 31 areread out in a unit of 6×2 (=mb) bits in the row direction and suppliedto the replacement section 32 (FIGS. 16 and 17).

The replacement section 32 replaces, for example, the 6×2 (=mb) codebits b₀, b₁, b₂, b₃, b₄, b₅, b₆, b₇, b₈, b₉, b₁₀ and b₁₁ read out fromthe memory 31 such that, as seen in FIG. 61B the 6×2 (=mb) code bits b₀to b₁₁ are allocated to 6×2 (=mb) symbol bits y₀, y₁, y₂, y₃, y₄, y₅,y₆, y₇, y₈, y₉, y₁₀ and y₁₁ of successive two (=b) symbols.

In particular, the replacement section 32 carries out replacement forallocating the code bits b₀ to b₁₁ to the symbol bits y₀ to y₁₁ as inthe case of FIG. 60B described above.

In particular, FIG. 61C illustrates an example of the replacement methodof an existing method where the LDPC code is an LDPC code having a codelength N of 16,200 bits and an encoding rate of 3/5 and besides themodulation method is 256QAM and the multiple b is 1.

Where the modulation method is 256QAM, 8 (=m) bits from among the codebits are mapped as one symbol to some of 256 signal points prescribed by256QAM.

Further, where the code length N is 16,200 bits and the multiple b is 1,the memory 31 (FIGS. 16 and 17) of the demultiplexer 25 has 8 columnsfor storing 8×1 (=mb) bits in the row direction and stores 16,200/(8×1)bits in the column direction.

In the demultiplexer 25, when the code bits of the LDPC code are writtenin the column direction of the memory 31 and writing of the 16,200 codebits (one codeword) ends, the code bits written in the memory 31 areread out in a unit of 8×1 (=mb) bits in the row direction and suppliedto the replacement section 32 (FIGS. 16 and 17).

The replacement section 32 replaces, for example, the 8×1 (=mb) codebits b₀, b₁, b₂, b₃, b₄, b₅, b₆, and b₇ read out from the memory 31 suchthat, as seen in FIG. 61C, the 8×1 (=mb) code bits b₀ to b₇ areallocated to 8×1 (=mb) symbol bits y₀, y₁, y₂, y₃, y₄, y₅, y₆ and y₇ ofsuccessive one (=b) symbols.

In particular, the replacement section 32 carries out replacement forallocating

the code bit b₀ to the symbol bit y₇,

the code bit b₁ to the symbol bit y₃,

the code bit b₂ to the symbol bit y₁,

the code bit b₃ to the symbol bit y₅,

the code bit b₄ to the symbol bit y₂,

the code bit b₅ to the symbol bit y₆,

the code bit b₆ to the symbol bit y₄, and

the code bit b₇ to the symbol bit y₀.

Now, a replacement process in accordance with an allocation rule(hereinafter referred to also as replacement process in accordance withthe new replacement method) is described.

FIGS. 62 to 64 are views illustrating the new replacement method.

In the new replacement method, the replacement section 32 of thedemultiplexer 25 carries out replacement of mb code bits in accordancewith an allocation rule determined in advance.

The allocation rule is a rule for allocating code bits of an LDPC codeto symbol bits. In the allocation rule, a group set which is acombination of a code bit group of code bits and a symbol bit group ofsymbol bits to which the code bits of the code bit group are allocatedand a bit number (hereinafter referred to also as group bit number) ofcode bits and symbol bits of the code bit group and the symbol bit groupof the group set are prescribed.

Here, the code bits are different in error probability thereamong andalso the symbol bits are different in error probability thereamong asdescribed above. The code bit group is a group into which the code bitsare grouped in accordance with the error probability and the symbol bitgroup is a group into which the symbol bits are grouped in accordancewith the error probability.

FIG. 62 illustrates code bit groups and symbol bit groups where the LDPCcode is an LDPC code having a code length N of 64,800 bits and anencoding rate of 2/3 and besides the modulation method is 256QAM and themultiple b is 2.

In this instance, 8×2 (=mb) code bits b₀ to b₁₅ read out from the memory31 can be grouped into five code bit groups Gb₁, Gb₂, Gb₃, Gb₄ and Gb₅as seen in FIG. 62A in accordance with the difference in errorprobability.

Here, the code bit group Gb_(i) is a group in which code bits belongingto the code bit group Gb_(i) have a better (lower) error probability asthe suffix i thereof has a lower value.

In FIG. 62A, to the code bit group Gb₁, the code bit b₀ belongs; to thecode bit group Gb₂, the code bit b₁ belongs; to the code bit group Gb₃,the code bits b₂ to b₉ belong; to the code bit group Gb₄, the code bitb₁₀ belongs; and to the code bit group Gb₅, the code bits b₁₁ to b₁₅belong.

Where the modulation method is 256QAM and the multiple b is 2, the 8×2(=mb) symbol bits y₀ to y₁₅ can be grouped into four symbol bit groupsGy₁, Gy₂, Gy₃ and Gy₄ as seen in FIG. 62B in accordance with thedifference in error probability.

Here, the symbol bit group Gy_(i) is a group in which symbol bitsbelonging to the symbol bit group Gy_(i) have a better error probabilityas the suffix i thereof has a lower value similarly to the code bitgroup.

In FIG. 62B, to the symbol bit group Gy₁, the symbol bits y₀, y₁, y₈ andy₉ belong; to the symbol bit group Gy₂, the symbol bits y₂, y₃, y₁₀ andy₁₁ belong; to the symbol bit group Gy₃, the symbol bits y₄, y₅, y₁₂ andy₁₃ belong; and to the symbol bit group Gy₄, the symbol bits y₆, y₇, y₁₄and y₁₅ belong.

FIG. 63 illustrates an allocation rule where the LDPC code is an LDPCcode having a code length N of 64,800 bits and an encoding rate of 2/3and besides the modulation method is 256QAM and the multiple b is 2.

In the allocation rule of FIG. 63, the combination of the code bit groupGb₁ and the symbol bit group Gy₄ is defined in the first from the leftof FIG. 63 as one group set. Further, the group bit number of the groupset is prescribed to 1 bit.

In the following description, a group set and a group bit number of thegroup set are collectively referred to as group set information. Forexample, the group set of the code bit group Gb₁ and the symbol bitgroup Gy₄ and 1 bit which is the group bit number of the group set aredescribed as group set information (Gb₁, Gy₄, 1).

In the allocation rule of FIG. 63, group set information (Gb₂, Gy₄, 1),(Gb₃, Gy₁, 3), (Gb₃, Gy₂, 1), (Gb₃, Gy₃, 2), (Gb₃, Gy₄, 2), (Gb₄, Gy₃,1), (Gb₅, Gy₁, 1), (Gb₅, Gy₂, 3) and (Gb₅, Gy₃, 1) is prescribed inaddition to the group set information (Gb₁, Gy₄, 1).

For example, the group set information (Gb₁, Gy₄, 1) signifies that onecode bit belonging to the code bit group Gb₁ is allocated to one symbolbit belonging to the symbol bit group Gy₄.

Accordingly, according to the allocation rule of FIG. 63, it isprescribed that,

depending upon the group set information (Gb₁, Gy₄, 1), one code bit ofthe code bit group Gb₁ which is best in error probability is allocatedto one symbol bit of the symbol bit group Gy₄ which is fourth best inerror probability, that

depending upon the group set information (Gb₂, Gy₄, 1), one code bit ofthe code bit group Gb₂ which is second best in error probability isallocated to one symbol bit of the symbol bit group Gy₄ which is fourthbest in error probability, that

depending upon the group set information (Gb₃, Gy₁, 3), three code bitsof the code bit group Gb₃ which is third best in error probability areallocated to three symbol bits of the symbol bit group Gy₁ which is bestin error probability, that

depending upon the group set information (Gb₃, Gy₂, 1), one code bit ofthe code bit group Gb₃ which is third best in error probability isallocated to one symbol bit of the symbol bit group Gy₂ which is secondbest in error probability, that

depending upon the group set information (Gb₃, Gy₃, 2), two code bits ofthe code bit group Gb₃ which is third best in error probability isallocated to two symbol bits of the symbol bit group Gy₃ which is thirdbest in error probability, that

depending upon the group set information (Gb₃, Gy₄, 2), two code bits ofthe code bit group Gb₃ which is third best in error probability isallocated to two symbol bits of the symbol bit group Gy₄ which is fourthbest in error probability, that

depending upon the group set information (Gb₄, Gy₃, 1), one code bit ofthe code bit group Gb₄ which is fourth best in error probability isallocated to one symbol bit of the symbol bit group Gy₃ which is thirdbest in error probability, that

depending upon the group set information (Gb₅, Gy₁, 1), one code bit ofthe code bit group Gb₅ which is fifth best in error probability isallocated to one symbol bit of the symbol bit group Gy₁ which is best inerror probability, that

depending upon the group set information (Gb₅, Gy₂, 3), three code bitsof the code bit group Gb₅ which is fifth best in error probability isallocated to three symbol bits of the symbol bit group Gy₂ which issecond best in error probability, and that

depending upon the group set information (Gb₅, Gy₃, 1), one code bit ofthe code bit group Gb₅ which is fifth best in error probability isallocated to one symbol bit of the symbol bit group Gy₃ which is thirdbest in error probability.

As described above, the code bit group is a group into which code bitsare grouped in accordance with the error probability, and the symbol bitgroup is a group into which symbol bits are grouped in accordance withthe error probability. Accordingly, also it can be considered that theallocation rule prescribes a combination of the error probability ofcode bits and the error probability of symbol bits to which the codebits are allocated.

In this manner, the allocation rule which prescribes a combination ofthe error probability of code bits and the error probability of symbolbits to which the code bits are allocated is determined such that thetolerance to errors (tolerance to noise) is made better, for example,through a simulation wherein the BER is measured or the like.

It is to be noted that, even if the allocation destination of a code bitof a certain code bit group is changed among bits of the same symbol bitgroup, the tolerance to errors is not (little) influenced thereby.

Accordingly, in order to improve the tolerance to errors, group setinformation which makes the BER (Bit Error Rate) including the errorfloor lower, in particular, combinations (group sets) of code bit groupsof code bits and symbol bit groups of symbol bits to which the code bitsof the code bit groups are to be allocated and the bit numbers (groupbit numbers) of the code bits of the code bit groups and the symbol bitgroups of the group sets and of the symbol bits, should be defined as anallocation rule, and replacement of the code bits should be carried outsuch that the code bits are allocated to the symbol bits in accordancewith the allocation rule.

However, a particular allocation method in regard to to which symboleach code bit should be allocated in accordance with the allocation ruleneed be determined in advance between the transmission apparatus 11 andthe reception apparatus 12 (FIG. 7).

FIG. 64 illustrates an example of replacement of code bits in accordancewith the allocation rule of FIG. 63.

In particular, FIG. 64A illustrates a first example of replacement ofcode bits in accordance with the allocation rule of FIG. 63 where theLDPC code is an LDPC code having a code length N of 64,800 bits and anencoding rate of 2/3 and besides the modulation method is 256QAM and themultiple b is 2.

Where the LDPC code is an LDPC code having a code length N of 64,800bits and an encoding rate of 2/3 and besides the modulation method is256QAM and the multiple b is 2, in the demultiplexer 25, code bitswritten in the memory 31 for (64,800/(8×2))×(8×2) bits in the columndirection×row direction are read out in a unit of 8×2 (=mb) bits in therow direction and are supplied to the replacement section 32 (FIGS. 16and 17).

The replacement section 32 replaces the 8×2 (=mb) code bits b₀ to b₁₅read out from the memory 31 in accordance with the allocation rule ofFIG. 63 such that the 8×2 (=mb) code bits b₀ to b₁₅ are allocated, forexample, to the 8×2 (=mb) symbol bits y₀ to y₁₅ of two (=b) successivesymbols as seen in FIG. 64A.

In particular, the replacement section 32 carries out replacement forallocating

the code bit b₀ to the symbol bit y₁₅,

the code bit b₁ to the symbol bit y₇,

the code bit b₂ to the symbol bit y₁,

the code bit b₃ to the symbol bit y₅,

the code bit b₄ to the symbol bit y₆,

the code bit b₅ to the symbol bit y₁₃,

the code bit b₅ to the symbol bit y₁₁,

the code bit b₇ to the symbol bit y₉,

the code bit b₈ to the symbol bit y₈,

the code bit b₉ to the symbol bit y₁₄,

the code bit b₁₀ to the symbol bit y₁₂,

the code bit b₁₁ to the symbol bit y₃,

the code bit b₁₂ to the symbol bit y₀,

the code bit b₁₃ to the symbol bit y₁₀,

the code bit b₁₄ to the symbol bit y₄, and

the code bit b₁₅ to the symbol bit y₂.

FIG. 64B illustrates a second example of replacement of code bits inaccordance with the allocation rule of FIG. 63 where the LDPC code is anLDPC code having a code length N of 64,800 bits and an encoding rate of2/3 and besides the modulation method is 256QAM and the multiple b is 2.

According to FIG. 64B, the replacement section 32 carries outreplacement for allocating the 8×2 (=mb) code bits b₀ to b₁₅ read outfrom the memory 31 in accordance with the allocation rule of FIG. 63 insuch a manner as to allocate

the code bit b₀ to the symbol bit y₁₅,

the code bit b₁ to the symbol bit y₁₄,

the code bit b₂ to the symbol bit y₈,

the code bit b₃ to the symbol bit y₅,

the code bit b₄ to the symbol bit y₆,

the code bit b₅ to the symbol bit y₄,

the code bit b₆ to the symbol bit y₂,

the code bit b₇ to the symbol bit y₁,

the code bit b₈ to the symbol bit y₉,

the code bit b₉ to the symbol bit y₇,

the code bit b₁₀ to the symbol bit y₁₂,

the code bit b₁₁ to the symbol bit y₃,

the code bit b₁₂ to the symbol bit y₁₃,

the code bit b₁₃ to the symbol bit y₁₀,

the code bit b₁₄ to the symbol bit y₀, and

the code bit b₁₅ to the symbol bit y₁₁.

Here, the allocation methods of the code bits b_(i) to the symbol bitsy_(i) illustrated in FIG. 64A and FIG. 64B observe the allocation ruleof FIG. 63 (follow the allocation rule).

FIG. 65 illustrates a result of a simulation of the BER (Bit Error Rate)in a case wherein a replacement process of the new replacement systemdescribed hereinabove with reference to FIGS. 62 to 64 is carried outand in another case wherein a replacement process described hereinabovewith reference to FIG. 60C from among the existing methods is carriedout.

In particular, FIG. 65 illustrates the BER where an LDPC code which isprescribed in the DVB-S.2 and has a code length N of 64,800 and anencoding rate of 2/3 is determined as an object and besides 256QAM isadopted as the modulation method and 2 is adopted as the multiple b.

It is to be noted that, in FIG. 65, the axis of abscissa indicates theE_(s)/N₀ and the axis of ordinate indicates the BER. Further, a roundmark represents the BER where a replacement process of the newreplacement method is carried out, and an asterisk (star mark)represents the BER where a replacement process of the existing method iscarried out.

From FIG. 65, it can be recognized that, according to the replacementprocess of the new replacement method, the error floor dropssignificantly in comparison with that of the replacement process of theexisting method and the tolerance to errors is improved.

It is to be noted that, while, in the present embodiment, thereplacement section 32 in the demultiplexer 25 carries out thereplacement process for code bits read out from the memory 31 for theconvenience of description, the replacement process can be carried outby controlling writing or reading out of code bits into or from thememory 31.

In particular, the replacement process can be carried out, for example,by controlling the address (read address) for reading out a code bitsuch that reading out of the code bits from the memory 31 is carried outin order of the code bits after the replacement.

Now, as a countermeasure for improving the tolerance to errors, a methodof adopting an LDPC code which lowers the error floor is available inaddition to the method which adopts a replacement process of thereplacement method which lowers the error floor.

Thus, the LDPC encoding section 21 (FIG. 8) can carry out encoding of anLDPC code having a code length N of 64,800 bits and an encoding rate rof 2/3 into an LDPC code of a high performance by adopting a paritycheck matrix initial value table which is different from the paritycheck matrix initial value tables prescribed in the DVB-S.2 standard andfrom which an appropriate parity check matrix H is determined and usinga parity check matrix determined from the parity check matrix initialvalue table.

Here, the appropriate parity check matrix H is a parity check matrixwhich satisfies a predetermined condition for making the BER (Bit ErrorRate) lower when a modulation signal of an LDPC code obtained from aparity check matrix is transmitted at a low E_(s)/N₀ (signal power tonoise power ratio per one symbol) or E_(b)/N₀ (signal power to noisepower ratio per one bit). Further, the LDPC code of a high performanceis an LDPC code obtained from an appropriate parity check matrix.

The appropriate parity check matrix H can be determined, for example, bycarrying out a simulation of the BER when a modulation signal of an LDPCcode obtained from various parity check matrices which satisfy apredetermined condition is transmitted at a low E_(s)/N₀.

The predetermined condition which the appropriate parity check matrix Hshould satisfy is, for example, that the result of an analysis obtainedby an analysis method of a performance of a code called densityevolution is good, that the parity check matrix H does not include aloop of elements of the value 1 called cycle 4, that the parity checkmatrix H does not include the cycle 6, and so forth.

Here, the density evolution and incorporation of the same are disclosed,for example, in S. Y. Chung, G. D. Forney, T. J. Richardson and R.Urbanke, “On the Design of Low-Density Parity-Check Codes within 0.0045dB of the Shannon Limit,” IEEE Communications Leggers, VOL. 5, NO. 2,February 2001.

For example, if the variance value of noise is gradually increased fromzero on an AWGN channel, then although the expected value of the errorprobability of an LDPC code is zero first, it becomes different fromzero if the variance value of noise becomes higher than a certainthreshold value (threshold).

According to the density evolution, the expected value of the errorprobability of the same becomes different from zero. By comparing thethreshold value of the variance value (hereinafter referred to asperformance threshold value) of noise, it can be determined whether ornot the performance of the LDPC code (appropriateness of the paritycheck matrix) is good. Here, as the performance threshold value, theE_(b)/N₀ when the BER begins to drop (decrease).

If a performance threshold value, obtained by analysis by densityevolution, regarding an LDPC code which is defined in the DVB-S.2standard and has a code length N of 64,800 and an encoding rate r of 2/3(such LDPC code is hereinafter referred to also as standard code) isrepresented by V, then in the simulation, an LDPC code (parity checkmatrix) which has a code length N of 64,800 and an encoding rate r of2/3 and exhibits a performance threshold value lower than V+Δ obtainedby adding a predetermined margin Δ to V was selected as the LDPC codehaving a good performance.

FIGS. 66 to 68 illustrate a parity check matrix initial value table forone of LDPC codes whose E_(b)/N₀ as the performance threshold value islower than V+Δ (LDPC code having a code length N of 64,800 and anencoding rate r of 2/3).

It is to be noted that FIG. 67 is a view continuing to FIG. 66, and FIG.68 is a view continuing to FIG. 67.

In a parity check matrix H determined from the parity check matrixinitial value table of FIGS. 66 to 68, neither the cycle 4 nor the cycle6 exist.

FIG. 69 illustrates a result of the simulation of the BER regarding anLDPC code of a parity check matrix H determined from the parity checkmatrix initial value table of FIGS. 66 to 68 (such LDPC code ishereinafter referred to also as proposed code).

In particular, FIG. 69 illustrates, where the modulation method is256QAM, the BER with respect to the E_(s)/N₀ of the standard code (inthe figure, the BER is indicated by a round mark) and the BER for theE_(s)/N₀ of the proposed code (in the figure, the BER is indicated by asquare mark).

From FIG. 69, it can be recognized that the proposed code is better inperformance than the standard code and that particularly the error flooris improved significantly.

It is to be noted that the predetermined condition which the appropriateparity check matrix H should satisfy can be determined suitably fromsuch a point of view as enhancement of the decoding performance of anLDPC code, facilitation (simplification) of a decoding process of anLDPC code, and so forth.

FIG. 70 is a block diagram showing an example of a configuration of thereception apparatus 12 of FIG. 7.

Referring to FIG. 70, the reception apparatus 12 is a data processingapparatus for receiving a modulation signal from the transmissionapparatus 11 (FIG. 7) and includes an orthogonal demodulation section51, a demapping section 52, a deinterleaver 53 and an LDPC decodingsection 56.

The orthogonal demodulation section 51 receives a modulation signal fromthe transmission apparatus 11 and carries out orthogonal demodulation,and then supplies symbols obtained as a result of the orthogonaldemodulation (values on the I and Q axes) to the demapping section 52.

The demapping section 52 carries out demapping of converting the signalpoints from the orthogonal demodulation section 51 to code bits of anLDPC code to be symbolized symbols and supplies the code bits to thedeinterleaver 53.

The deinterleaver 53 includes a multiplexer (MUX) 54 and a column twistdeinterleaver 55 and carries out deinterleave of the symbols of thesymbol bits from the demapping section 52.

In particular, the multiplexer 54 carries out a reverse replacementprocess (reverse process to the replacement process) corresponding tothe replacement process carried out by the demultiplexer 25 of FIG. 8for the symbols of the symbol bits from the demapping section 52, thatis, a reverse replacement process of returning the positions of the codebits (symbol bits) of the LDPC codes replaced by the replacement processto the original positions. Then, the multiplexer 54 supplies an LDPCcode obtained as a result of the reverse replacement process to thecolumn twist deinterleaver 55.

The column twist deinterleaver 55 carries out column twist deinterleave(reverse process to the column twist interleave) corresponding to thecolumn twist interleave as the re-arrangement process carried out by thecolumn twist interleaver 24 of FIG. 8, that is, for example, columntwist deinterleave as a reverse re-arrangement process of returning thearrangement of the code bits of the LDPC code having an arrangementchanged by the column twist interleave as the re-arrangement process tothe original arrangement, for the LDPC code from the multiplexer 54.

In particular, the column twist deinterleaver 55 carries out columntwist deinterleave by writing the code bits of the LDPC code into andreading out the written code bits from the memory for deinterleave, thememory being configured similarly to the memory 31 shown in FIG. 22 andso forth.

It is to be noted that, in the column twist deinterleaver 55, writing ofthe code bits is carried out in the row direction of the memory fordeinterleave using read addresses upon reading out the codes from thememory 31 as write addresses. Meanwhile, readout of the code bits iscarried out in the column direction of the memory for deinterleave usingthe write addresses upon writing of the code bits into the memory 31 asread addresses.

The LDPC codes obtained as a result of the column twist interleave aresupplied from the column twist deinterleaver 55 to the LDPC decodingsection 56.

Here, while the LDPC code supplied from the demapping section 52 to thedeinterleaver 53 has been obtained by the parity interleave, columntwist interleave and replacement process carried out in this ordertherefor, the deinterleaver 53 carries out only a reverse replacementprocess corresponding to the replacement process and column twistdeinterleave corresponding to the column twist interleave. Accordingly,parity deinterleave corresponding to the parity interleave (processreverse to the parity interleave), that is, the parity deinterleavereturning the arrangement of the code bits of the LDPC codes, whosearrangement has been varied by the parity interleave, to the originalarrangement, is not carried out.

Accordingly, the LDPC code for which the reverse replacement process andthe column twist deinterleave have been carried out but the paritydeinterleave has not been carried out is supplied from the (column twistdeinterleaver 55 of the) deinterleaver 53 to the LDPC decoding section56.

The LDPC decoding section 56 carries out LDPC decoding of the LDPC codefrom the deinterleaver 53 using a conversion parity check matrix,obtained by carrying out at least column replacement corresponding tothe parity interleave for the parity check matrix H used for the LDPCencoding by the LDPC encoding section 21 of FIG. 8, and outputs dataobtained as a result of the LDPC decoding as a decoding result of theobject data.

FIG. 71 is a flow chart illustrating a reception process carried out bythe reception apparatus 12 of FIG. 70.

The orthogonal demodulation section 51 receives a modulation signal fromthe transmission apparatus 11 at step S111. Then, the processingadvances to step S112, at which the orthogonal demodulation section 51carries out orthogonal demodulation of the modulation signal. Theorthogonal demodulation section 51 supplies signal points obtained as aresult of the orthogonal demodulation to the demapping section 52,whereafter the processing advances from step S112 to step S113.

At step S113, the demapping section 52 carries out demapping ofconverting the signal points from the orthogonal demodulation section 51into symbols and supplies the code bits to the deinterleaver 53,whereafter the processing advances to step S114.

At step S114, the deinterleaver 53 carries out deinterleave of thesymbols of the symbol bits from the demapping section 52, whereafter theprocessing advances to step S115.

In particular, at step S114, the multiplexer 54 in the deinterleaver 53carries out a reverse replacement process for the symbols of the symbolbits from the demapping section 52 and supplies LDPC code obtained as aresult of the reverse replacement process to the column twistdeinterleaver 55.

The column twist deinterleaver 55 carries out column twist deinterleavefor the LDPC code from the multiplexer 54 and supplies an LDPC codeobtained as a result of the column twist deinterleave to the LDPCdecoding section 56.

At step S115, the LDPC decoding section 56 carries out LDPC decoding ofthe LDPC code from the column twist deinterleaver 55 using a conversionparity check matrix obtained by carrying out at least column replacementcorresponding to the parity interleave for the parity check matrix Hused for the LDPC encoding by the LDPC encoding section 21 of FIG. 8,and outputs data obtained by the LDPC decoding as a decoding result ofthe object data. Thereafter, the processing is ended.

It is to be noted that the reception process of FIG. 71 is carried outrepetitively.

Also in FIG. 70, the multiplexer 54 for carrying out the reversereplacement process and the column twist deinterleaver 55 for carryingout the column twist deinterleave are configured separately from eachother for the convenience of description similarly as in the case ofFIG. 8. However, the multiplexer 54 and the column twist deinterleaver55 can be configured integrally with each other.

Further, where the transmission apparatus 11 of FIG. 8 does not carryout the column twist interleave, there is no necessity to provide thecolumn twist deinterleaver 55 in the reception apparatus 12 of FIG. 70.

Now, the LDPC decoding carried out by the LDPC decoding section 56 ofFIG. 70 is further described.

The LDPC decoding section 56 of FIG. 70 carries out LDPC decoding of anLDPC code, for which the reverse replacement process and the columntwist deinterleave have been carried out but the parity deinterleave hasnot been carried out, from the column twist deinterleaver 55 asdescribed above using a conversion parity check matrix obtained bycarrying out at least column replacement corresponding to the parityinterleave for the parity check matrix H used for the LDPC encoding bythe LDPC encoding section 21 of FIG. 8.

Here, LDPC decoding which can suppress the operation frequency within asufficiently implementable range while suppressing the circuit scale bycarrying out the LDPC decoding using the conversion parity check matrixhas been proposed formerly (refer to, for example, Japanese PatentLaid-Open No. 2004-343170).

Thus, the formerly proposed LDPC decoding which uses a conversion paritycheck matrix is described first with reference to FIGS. 72 to 75.

FIG. 72 shows an example of the parity check matrix H of an LDPC codewhose code length N is 90 and encoding rate is 2/3.

It is to be noted that, in FIG. 72, 0 is represented by a period (.)(this similarly applies also to FIGS. 73 and 74 hereinafter described).

In the parity check matrix H of FIG. 72, the parity matrix has astaircase structure.

FIG. 73 illustrates a parity check matrix H′ obtained by applying rowreplacement of an expression (11) and column replacement of anexpression (12) to the parity check matrix H of FIG. 72.Row replacement: 6s+t+1th row→5t+s+1th row  (11)Column replacement: 6x+y+61th column→5y+x+61th column  (12)

However, in the expressions (11) and (12), s, t, x and y are integerswithin the ranges of 0≦s<5, 0≦t<6, 0≦x<5 and 0≦t<6, respectively.

According to the row replacement of the expression (11), the replacementis carried out in such a manner that the 1st, 7th, 13th, 19th and 25throws each of whose numbers indicates a remainder of 1 where it isdivided by 6 are replaced to the 1st, 2nd, 3rd, 4th and 5th rows, andthe 2nd, 8th, 14th, 20th and 26th rows each of whose numbers indicates aremainder of 2 where it is divided by 6 are replaced to 6th, 7th, 8th,9th and 10th rows.

On the other hand, according to the column replacement of the expression(12), the replacement is carried out for the 61st and succeeding columns(parity matrix) such that the 61st, 67th, 73rd, 79th and 85th columnseach of whose numbers indicates a remainder of 1 where it is divided by6 are replaced to 61st, 62nd, 63rd, 64th and 65th columns, and the 62nd,68th, 74th, 80th and 86th columns each of whose numbers indicates aremainder of 2 where it is divided by 6 are replaced to 66th, 67th,68th, 69th and 70th columns.

A matrix obtained by carrying out replacement of the rows and thecolumns for the parity check matrix H of FIG. 72 is a parity checkmatrix H′ of FIG. 73.

Here, even if the row replacement of the parity check matrix H iscarried out, this does not have an influence on the arrangement of thecode bits of the LDPC code.

Meanwhile, the column replacement of the expression (12) corresponds toparity interleave when the information length K, the unit column numberP of the cyclic structure and the devisor q (=M/P) of the parity lengthM (here, 30) in the parity interleave of interleaving the K+qx+y+1thcode bit to the position of the K+Py+x+1th code bit are set to 60, 5 and6, respectively.

If the parity check matrix H′ (hereinafter referred to suitably asreplacement parity check matrix) of FIG. 73 is multiplied by a result ofreplacement same as that of the expression (12) for the LDPC code of theparity check matrix H (hereinafter referred to suitably as originalparity check matrix) of FIG. 72, then the 0 vector is outputted. Inparticular, where a row vector obtained by applying the columnreplacement of the expression (12) for the row vector c as the LDPC code(one codeword) of the original parity check matrix H is represented byc′, since Hc^(T) becomes the 0 vector on the basis of the characteristicof the parity check matrix, also H′c′^(T) naturally becomes the 0vector.

From the foregoing, the conversion parity check matrix H′ of FIG. 73becomes the parity check matrix of an LDPC code c′ obtained by carryingout the column replacement of the expression (12) for the LDPC code c ofthe original parity check matrix H.

Accordingly, by carrying out the column replacement of the expression(12) for the LDPC code c of the original parity check matrix H, decoding(LDPC decoding) the LDPC code c′ after the column replacement using theparity check matrix H′ of FIG. 73 and then carrying out reversereplacement to the column replacement of the expression (12) for resultof decoding, a decoding result similar to that obtained where the LDPCcode of the original parity check matrix H is decoded using the paritycheck matrix H can be obtained.

FIG. 74 shows the conversion parity check matrix H′ of FIG. 73 wherein aspace is provided between units of 5×5 matrices.

In FIG. 74, the conversion parity check matrix H′ is represented by acombination of a unit matrix of 5×5 elements, another matrix(hereinafter referred to suitably as quasi unit matrix) whichcorresponds to the unit matrix whose element or elements of 1 arechanged into an element or elements of 0, a further matrix (hereinafterreferred to suitably as shift matrix) which corresponds to the unitmatrix or quasi unit matrix after it is cyclically shifted (cyclicshift), a still further matrix (hereinafter referred to suitably as summatrix) of two or more of the unit matrix, quasi unit matrix and shiftmatrix, and a 0 matrix of 5×5 elements.

It can be regarded that the conversion parity check matrix H′ of FIG. 74is composed of a unit matrix, a quasi unit matrix, a shift matrix, a summatrix and a 0 matrix of 5×5 elements. Therefor, the matrices of 5×5elements which compose the conversion parity check matrix H′ arehereinafter referred to as component matrices.

For decoding of an LDPC code represented by a parity check matrixrepresented by a matrix of P×P components, an architecture which carriesout check node mathematical operation and variable node mathematicaloperation simultaneously for P check nodes and P variable nodes can beused.

FIG. 75 is a block diagram showing an example of a configuration of adecoding apparatus which carries out such decoding as just described.

In particular, FIG. 75 shows an example of a configuration of a decodingapparatus which carries out decoding of LDPC codes of the originalparity check matrix H of FIG. 72 using the conversion parity checkmatrix H′ of FIG. 74 obtained by carrying out at least the columnreplacement of the expression (12).

The decoding apparatus of FIG. 75 includes an edge data storage memory300 including six FIFOs 300 ₁ to 300 ₆, a selector 301 for selecting theFIFOs 300 ₁ to 300 ₆, a check node calculation section 302, two cyclicshift circuits 303 and 308, an edge data storage memory 304 including 18FIFOs 304 ₁ to 304 ₁₈, a selector 305 for selecting the FIFOs 304 ₁ to304 ₁₈, a reception data memory 306 for storing reception information, avariable node calculation section 307, a decoded word calculationsection 309, a reception data re-arrangement section 310, and a decodeddata re-arrangement section 311.

First, a storage method of data into the edge data storage memories 300and 304 is described.

The edge data storage memory 300 includes the six FIFOs 300 ₁ to 300 ₆the number of which is equal to a quotient when the row number 30 of theconversion parity check matrix H′ of FIG. 74 is divided by the rownumber 5 of the component matrices. Each of the FIFOs 300 _(y) (y=1, 2,. . . , 6) has a plurality of stages of storage regions such thatmessages corresponding to five edges whose number is equal to the numberof rows and the number of columns of the component matrices can be readout from or written into the storage regions of each stage at the sametime. Further, the number of stages of the storage regions of each FIFO300 _(y) is nine which is the maximum number of is (Hamming weight) inthe row direction of the conversion parity check matrix of FIG. 74.

In the FIFO 300 ₁, data (messages v_(i) from variable nodes)corresponding to the positions of the value 1 in the first to fifth rowsof the conversion parity check matrix H′ of FIG. 74 are stored in aclosed form in the horizontal direction in the individual rows (in theform wherein 0 is ignored). In particular, if an element in the j row ofthe ith column is represented as (j, i), then in the storage regions atthe first stage of the FIFO 300 ₁, data corresponding to the positionsof the value 1 of the unit matrix of 5×5 elements from (1, 1) to (5, 5)of the conversion parity check matrix H′ are stored. In the storageregions at the second stage, data corresponding to the positions of thevalue 1 of a shift matrix from (1, 21) to (5, 25) of the conversionparity check matrix H′ (a shift matrix obtained by cyclically shiftingthe unit matrix of 5×5 elements by three in the rightward direction).Also in the storage regions at the third to eighth stages, data arestored in an associated relationship with the conversion parity checkmatrix H′. Then, in the storage regions at the ninth stage, datacorresponding to the positions of the value of a shift matrix of (1, 86)to (5, 90) of the conversion parity check matrix H′ (a shift matrixobtained by replacing the value 1 in the first row of the unit matrix of5×5 elements with the value 0 and then cyclically shifting the unitmatrix after the replacement by one in the leftward direction) arestored.

In the FIFO 300 ₂, data corresponding to the positions of the value 1from the sixth to tenth rows of the conversion parity check matrix H′ ofFIG. 74 are stored. In particular, in the storage region at the firststage of the FIFO 300 ₂, data corresponding to the positions of thevalue 1 of a first shift matrix which forms a sum matrix from (6, 1) to(10, 5) of the conversion parity check matrix H′ (a sum matrix which isthe sum of a first shift matrix obtained by cyclically shifting the unitmatrix of 5×5 elements by one in the rightward direction and a secondshift matrix obtained by cyclically shifting the unit matrix of 5×5elements by two in the rightward direction) are stored. Further, in thestorage region at the second stage, data corresponding to the positionsof the value 1 of the second shift matrix which forms the sum matrixfrom (6, 1) to (10, 5) of the conversion parity check matrix H′ arestored.

In particular, with regard to a component matrix whose weight is 2 ormore, where the component matrix is represented in the form of the sumof plural ones from among a unit matrix of P×P elements having theweight 1, a quasi unit matrix which corresponds to the unit matrix whoseone or more elements having the value 1 are replaced with 0 and a shiftmatrix obtained by cyclically shifting the unit matrix or the quasi unitmatrix, data corresponding to the positions of the value 1 of the unitmatrix, quasi unit matrix or shift matrix whose weight is (messagescorresponding to edges belonging to the unit matrix, quasi unit matrixor shift matrix) are stored into the same address (same FIFO from amongthe FIFOs 300 ₁ to 300 ₆).

Also in the storage regions at the third to ninth stages, data arestored in an associated relationship with the conversion parity checkmatrix H′.

Also the FIFOs 300 ₃ to 300 ₆ store data in an associated relationshipwith the conversion parity check matrix H′.

The edge data storage memory 304 includes 18 FIFOs 304 ₁ to 304 ₁₈ thenumber of which is equal to the quotient when the column number 90 ofthe conversion parity check matrix H′ is divided by the column number 5of the component matrix. Each edge data storage memory 304 _(x) (x=1, 2,. . . , 18) includes a plurality of stages of storage regions, andmessages corresponding to five edges the number of which is equal to thenumber of rows and the number of columns of the conversion parity checkmatrix H′ can be read out from or written into the storage regions ofeach stage at the same time.

In the FIFO 304 ₁, data corresponding to the positions of the value 1from the first to fifth columns of the conversion parity check matrix H′of FIG. 74 (messages u_(j) from the check nodes) are stored in a closedform in the vertical direction in the individual columns (in the formwherein 0 is ignored). In particular, in the storage regions at thefirst stage of the FIFO 304 ₁, data corresponding to the positions ofthe value 1 of the unit matrix of 5×5 elements from (1, 1) to (5, 5) ofthe conversion parity check matrix H′ are stored. In the storage regionsat the second stage, data corresponding to the positions of the value ofa first shift matrix which forms a sum matrix from (6, 1) to (10, 5) ofthe vertical parity check matrix H′ (a sum matrix which is the sum of afirst shift matrix obtained by cyclically shifting the unit matrix of5×5 elements by one to the right and a second shift matrix obtained bycyclically shifting the unit matrix of 5×5 elements by two to the right)are stored. Further, in the storage regions at the third stage, datacorresponding to the positions of the value 1 of the second shift matrixwhich forms the sum matrix from (6, 1) to (10, 5) of the vertical paritycheck matrix H′.

In particular, with regard to a component matrix whose weight is 2 ormore, where the component matrix is represented in the form of the sumof plural ones from among a unit matrix of P×P elements having theweight 1, a quasi unit matrix which corresponds to the unit matrix whoseone or more elements having the value 1 are replaced with 0 and a shiftmatrix obtained by cyclically shifting the unit matrix or the quasi unitmatrix, data corresponding to the positions of the value 1 of the unitmatrix, quasi unit matrix or shift matrix whose weight is (messagescorresponding to edges belonging to the unit matrix, quasi unit matrixor shift matrix) are stored into the same address (same FIFO from amongthe FIFOs 304 ₁ to 304 ₁₈).

Also with regard to the storage regions at the fourth and fifth stages,data are stored in an associated relationship with the conversion paritycheck matrix H′. The number of stages of the storage regions of the FIFO304 ₁ is 5 which is a maximum number of the number of is (Hammingweight) in the row direction in the first to fifth columns of theconversion parity check matrix H′.

Also the FIFOs 304 ₂ and 304 ₃ store data in an associated relationshipwith the conversion parity check matrix H′ similarly, and each length(stage number) of the FIFOs 304 ₂ and 304 ₃ is 5. Also the FIFOs 304 ₄to 304 ₁₂ store data in an associated relationship with the conversionparity check matrix H′ similarly, and each length of the FIFOs 304 ₄ to304 ₁₂ is 3. Also the FIFOs 304 ₁₃ to 304 ₁₈ store data in an associatedrelationship with the conversion parity check matrix H′ similarly, andeach length of the FIFOs 304 ₁₃ to 304 ₁₈ is 2.

Now, operation of the decoding apparatus of FIG. 75 is described.

The edge data storage memory 300 includes the six FIFOs 300 ₁ to 300 ₆,and FIFOs into which data are to be stored are selected from among theFIFOs 300 ₁ to 300 ₆ in accordance with information (Matrix data) D312representing to which row of the conversion parity check matrix H′ fivemessages D311 supplied from the cyclic shift circuit 308 at thepreceding stage belong. Then, the five messages D311 are storedcollectively and in order into the selected FIFOs. Further, when dataare to be read out, the edge data storage memory 300 reads out fivemessages D300 ₁ in order from the FIFO 300 ₁ and supplies the fivemessages D300 ₁ to the selector 301 at the succeeding stage. After thereading out of the messages from the FIFO 300 ₁ ends, the edge datastorage memory 300 reads out the messages in order also from the FIFOs330 ₂ to 300 ₆ and supplies the read out messages to the selector 301.

The selector 301 selects the five messages from that FIFO from whichdata are currently read out from among the FIFOs 300 ₁ to 300 ₆ inaccordance with a select signal D301 and supplies the five messages asmessages D302 to the check node calculation section 302.

The check node calculation section 302 includes five check nodecalculators 302 ₁ to 302 ₅ and carries out the check node mathematicaloperation in accordance with the expression (7) using the messages D302(D302 ₁ to D302 ₅) (messages v_(i) of the expression (7)) suppliedthereto through the selector 301. Then, the check node calculationsection 302 supplies five messages D303 (D303 ₁ to D303 ₅) (messagesu_(j) of the expression (7)) obtained as a result of the check nodemathematical operation to the cyclic shift circuit 303.

The cyclic shift circuit 303 cyclically shifts the five messages D303 ₁to 303 ₅ determined by the check node calculation section 302 based oninformation (Matrix data) D305 regarding by what number of original unitmatrices the corresponding edges are cyclically shifted in theconversion parity check matrix H′, and supplies a result of the cyclicshift as a message D304 to the edge data storage memory 304.

The edge data storage memory 304 includes 18 FIFOs 304 ₁ to 304 ₁₈. Theedge data storage memory 304 selects a FIFO into which data are to bestored from among the FIFOs 304 ₁ to 304 ₁₈ in accordance with theinformation D305 regarding to which row of the conversion parity checkmatrix H′ the five messages D304 supplied from the cyclic shift circuit303 at the preceding stage belong and collectively stores the fivemessages D304 in order into the selected FIFO. On the other hand, whendata are to be read out, the edge data storage memory 304 reads out fivemessages D306 ₁ in order from the FIFO 304 ₁ and supplies the messagesD306 ₁ to the selector 305 at the succeeding stage. After the readingout of data from the FIFO 304 ₁ ends, the edge data storage memory 304reads out messages in order also from the FIFOs 304 ₂ to 304 ₁₈ andsupplies the messages to the selector 305.

The selector 305 selects the five messages from the FIFO from which dataare currently read out from among the FIFOs 304 ₁ to 304 ₁₈ inaccordance with a select signal D307 and supplies the selected messagesas messages D308 to the variable node calculation section 307 and thedecoded word calculation section 309.

On the other hand, the reception data re-arrangement section 310 carriesout the column replacement of the expression (12) to re-arrange an LDPCcode D313 received through a communication path and supplies there-arranged LDPC code D313 as reception data D314 to the reception datamemory 306. The reception data memory 306 calculates and stores areception LLR (logarithmic likelihood ratio) from the reception dataD314 supplied thereto from the reception data re-arrangement section 310and collects and supplies every five ones of the reception LLRs asreception values D309 to the variable node calculation section 307 andthe decoded word calculation section 309.

The variable node calculation section 307 includes five variable nodecalculators 307 ₁ to 307 ₅ and carries out variable node mathematicaloperation in accordance with the expression (1) using the messages D308(308 ₁ to 308 ₅) (messages u_(j) of the expression (1)) supplied theretothrough the selector 305 and the five reception values D309 (receptionvalues u_(Oi) of the expression (1)) supplied thereto from the receptiondata memory 306. Then, the variable node calculation section 307supplies messages D310 (D301 ₁ to D310 ₅) (messages v_(i) of theexpression (1)) obtained as a result of the mathematical operation tothe cyclic shift circuit 308.

The cyclic shift circuit 308 cyclically shifts messages D310 ₁ to D310 ₅calculated by the variable node calculation section 307 based oninformation regarding by what number of original unit matrices thecorresponding edge is cyclically shifted in the conversion parity checkmatrix H′, and supplies a result of the cyclic shifting as a messageD311 to the edge data storage memory 300.

By carrying out the sequence of operations described above, decoding inone cycle of an LDPC code can be carried out. In the decoding apparatusof FIG. 75, after an LDPC code is decoded by a predetermined number oftimes, a final decoding result is determined by the decoded wordcalculation section 309 and the decoded data re-arrangement section 311and then outputted.

In particular, the decoded word calculation section 309 includes fivedecoded word calculators 309 ₁ to 309 ₅ and acts as a final stage in aplurality of cycles of decoding to calculate a decoding result (decodedword) in accordance with the expression (5) using the five messages D308(D308 ₁ to D308 ₅) (messages u_(j) of the expression (5)) outputted fromthe selector 305 and the five reception values D309 (reception valuesu_(Oi) of the expression (5)) outputted from the reception data memory306. Then, the decoded word calculation section 309 supplies decodeddata D315 obtained as a result of the calculation to the decoded datare-arrangement section 311.

The decoded data re-arrangement section 311 carries out reversereplacement to the column replacement of the expression (12) for thedecoded data D315 supplied thereto from the decoded word calculationsection 309 to re-arrange the order of the decoded data D315 and outputsthe re-arranged decoded data D315 as a decoding result D316.

As described above, by applying one or both of row replacement andcolumn replacement to a parity check matrix (original parity checkmatrix) to convert the parity check matrix into a parity check matrix(conversion parity check matrix) which can be represented by acombination of a unit matrix of P×P elements, a quasi unit matrix whichcorresponds to the unit matrix whose element or elements of 1 arechanged into an element or elements of 0, a shift matrix whichcorresponds to the unit matrix or quasi unit matrix after it iscyclically shifted, a sum matrix of two or more of the unit matrix,quasi unit matrix and shift matrix, and a 0 matrix of P×P elements asdescribed above, it becomes possible to adopt for LDPC code decoding anarchitecture which carries out check node mathematical operation andvariable node mathematical operation simultaneously for P check nodesand P variable nodes. Consequently, by carrying out the nodemathematical operation simultaneously for P nodes, it is possible tosuppress the operation frequency within an implementable range to carryout LDPC decoding.

The LDPC decoding section 56 which composes the reception apparatus 12of FIG. 70 carries out check node mathematical operation and variablenode mathematical operation simultaneously for P check nodes and Pvariable nodes to carry out LDPC decoding similarly to the decodingapparatus of FIG. 75.

In particular, it is assumed now to simplify description that the paritycheck matrix of an LDPC code outputted from the LDPC encoding section 21which composes the transmission apparatus 11 of FIG. 8 is, for example,the parity check matrix H wherein the parity matrix has a staircasestructure shown in FIG. 72. In this instance, the parity interleaver 23of the transmission apparatus 11 carries out parity interleave forinterleaving the K+qx+y+1th code bit to the position of the K+Py+x+1thcode bit with the information length K set to 60, with the unit columnnumber P of the cyclic structure set to 5 and with the devisor q (=M/P)of the parity length M to 6.

Since this parity interleave corresponds to the column replacement ofthe expression (12), the LDPC decoding section 56 need not carry out thecolumn replacement of the expression (12).

Therefore, in the reception apparatus 12 of FIG. 70, an LDPC code forwhich parity deinterleave has not been carried out, that is, an LDPCcode in a state wherein the column replacement of the expression (12) iscarried out, is supplied from the column twist deinterleaver 55 to theLDPC decoding section 56 as described above. The LDPC decoding section56 carries out processing similar to that of the decoding apparatus ofFIG. 75 except that the column replacement of the expression (12) is notcarried out.

In particular, FIG. 76 shows an example of a configuration of the LDPCdecoding section 56 of FIG. 70.

Referring to FIG. 76, the LDPC decoding section 56 is configuredsimilarly to that of the decoding apparatus of FIG. 75 except that thereception data re-arrangement section 310 of FIG. 75 is not provided andcarries out processing similar to that of the decoding apparatus of FIG.75 except that the column replacement of the expression (12) is notcarried out. Therefore, description of the LDPC decoding section 56 isomitted herein.

Since the LDPC decoding section 56 can be configured without includingthe reception data re-arrangement section 310 as described above, it canbe reduced in scale in comparison with the decoding apparatus of FIG.75.

It is to be noted that, while, in FIGS. 72 to 76, it is assumed that thecode length N of the LDPC code is 90; the information length K is 60;the unit column number P (row number and column number of a componentmatrix) of the cyclic structure is 5; and the devisor q (=M/P) of theparity length M is 6, for simplified description, the code length N,information length K, unit column number P of the cyclic structure andthe devisor q (=M/P) are not individually limited to the specific valuesgiven above.

In particular, while the LDPC encoding section 21 in the transmissionapparatus 11 of FIG. 8 outputs an LDPC code wherein, for example, thecode length N is 64,800 or 16,200, the information length K is N−Pq(=N−M), the unit column number P of the cyclic structure is 360 and thedevisor q is M/P, the LDPC decoding section 56 of FIG. 76 can be appliedalso where LDPC decoding is carried out by carrying out the check nodemathematical operation and the variable node mathematical operationsimultaneously for P check nodes and P variable nodes in regard to suchan LDPC code as just described.

While the series of processes described above can be executed byhardware, it may otherwise be executed by software. Where the series ofprocesses is executed by software, a program which constructs thesoftware is installed into a computer for universal use or the like.

FIG. 77 shows an example of a configuration of an embodiment of acomputer into which a program for executing the series of processesdescribed hereinabove is installed.

The program can be recorded in advance on a hard disk 705 or in a ROM703 as a recording medium built in the computer.

Or, the program can be stored (recorded) temporarily or permanently onor in a removable recording medium 711 such as a flexible disk, a CD-ROM(Compact Disc Read Only Memory), an MO (Magneto Optical) disc, a DVD(Digital Versatile Disc), a magnetic disc or a semiconductor memory.Such a removable recording medium 711 as just described can be providedas so-called package software.

It is to be noted that the program not only can be installed from such aremovable recording medium 711 as described above into the computer butalso can be installed into the hard disk 705 built in the computer whereit is transferred thereto and received by a communication section 708.In this instance, the program may be transferred to the computer bywireless communication from a download site through an artificialsatellite for digital satellite broadcasting or transferred to thecomputer by wire communication through a network such as a LAN (LocalArea Network) or the Internet.

The computer has a CPU (Central Processing Unit) 702 built therein. Aninput/output interface 7410 is connected to the CPU 702 by a bus 701,and if an instruction is inputted to the CPU 702 through theinput/output interface 710 when an inputting section 707 configured froma keyboard, a mouse, a microphone and so forth is operated by a user orin a like case, the CPU 702 executes the program stored in the ROM (ReadOnly Memory) 703. Or, the CPU 702 loads a program stored on the harddisk 705, a program transferred from a satellite or a network, receivedby the communication section 708 and installed in the hard disk 705 or aprogram read out from the removable recording medium 711 loaded in adrive 709 and installed in the hard disk 705 into a RAM (Random AccessMemory) 704 and executes the program. Consequently, the CPU 702 carriesout processing in accordance with the flow chart described hereinaboveor processing carried out by the configuration of the block diagramdescribed hereinabove. Then, the CPU 702 outputs a result of theprocessing from an outputting section 706 configured from an LCD (LiquidCrystal Display), a speaker and so forth and transmits the processingresult from the communication section 708 through the input/outputinterface 710 or records the processing result on the hard disk 705 asoccasion demands.

Here, in the present specification, processing steps which describe theprogram for causing the computer to carry out various processes need notnecessarily be processed in a time series in accordance with the orderdescribed as a flow chart but include those processes to be executed inparallel or individually (for example, parallel processes or processesby an object).

Further, the program may be processed by a single computer or may beprocessed by distributed processing by a plurality of computers.Further, the program may be transferred to and executed by a computer ata remote place.

Now, a process for LDPC encoding by the LDPC encoding section 21 of thetransmission apparatus 11 is described further.

For example, in the DVB-S.2 standard, LDPC encoding of the two differentcode lengths N of 64,800 bits and 16,200 bits are prescribed.

And, for the LDPC code whose code length N is 64,800 bits, the 11encoding rates 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9 and 9/10are prescribed, and for the LDPC code whose code length N is 16,200bits, the encoding rates 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6 and8/9 are prescribed.

The LDPC encoding section 21 carries out encoding (error correctionencoding) into LDPC codes of the different encoding rates whose codelength N is 64,800 bits or 16,200 bits in accordance with a parity checkmatrix H prepared for each code length N and for each encoding rate.

In particular, the LDPC encoding section 21 stores a parity check matrixinitial value table hereinafter described for producing a parity checkmatrix H for each code length N and for each encoding rate.

Here, in the DVB-S.2 standard, LDPC codes of the two different codelengths N of 64,800 bits and 16,200 bits are prescribed as describedhereinabove, and the 11 different encoding rates are prescribed for theLDPC code whose code length N is 64,800 bits and the 10 differentencoding rates are prescribed for the LDPC code whose code length N is16,200 bits.

Accordingly, where the transmission apparatus 11 is an apparatus whichcarries out processing in compliance with the DVB-S.2 standard, paritycheck matrix initial value tables individually corresponding to the 11different encoding rates for the LDPC code whose code length N is 64,800bits and parity check matrix initial value tables individuallycorresponding to the 10 different encoding rates for the LDPC code whosecode length N is 16,200 bits are stored in the LDPC encoding section 21.

The LDPC encoding section 21 sets a code length N and an encoding rate rfor LDPC codes, for example, in response to an operation of an operator.The code length N and the encoding rate r set by the LDPC encodingsection 21 are hereinafter referred to suitably as set code length N andset encoding rate r, respectively.

The LDPC encoding section 21 places, based on the parity check matrixinitial value tables corresponding to the set code length N and the setencoding rate r, elements of the value 1 of an information matrix H_(A)corresponding to an information length K (=Nr=code length N−paritylength M) corresponding to the set code length N and the set encodingrate r in a period of 360 columns (unit column number P of the cyclicstructure) in the column direction to produce a parity check matrix H.

Then, the LDPC encoding section 21 extracts information bits for theinformation length K from object data which are an object oftransmission such as image data or sound data supplied from thetransmission apparatus 11. Further, the LDPC encoding section 21calculates parity bits corresponding to the information bits based onthe parity check matrix H to produce a codeword (LDPC code) for one codelength.

In other words, the LDPC encoding section 21 successively carries outmathematical operation of a parity bit of the codeword c which satisfiesthe following expression.Hc^(T)=0

Here, in the expression above, c indicates a row vector as the codeword(LDPC code), and c^(T) indicates inversion of the row vector c.

Where, from within the row vector c as an LDPC code (one codeword), aportion corresponding to the information bits is represented by a rowvector A and a portion corresponding to the parity bits is representedby a row vector T, the row vector c can be represented by an expressionc=[A|T] from the row vector A as the information bits and the row vectorT as the parity bits.

Meanwhile, the parity check matrix H can be represented, from theinformation matrix H_(A) of those of the code bits of the LDPC codewhich correspond to the information bits and the parity matrix H_(T) ofthose of the code bits of the LDPC code which correspond to the paritybits by an expression H=[H_(A)|H_(T)] (matrix wherein the elements ofthe information matrix H_(A) are elements on the left side and theelements of the parity matrix H_(T) are elements on the right side).

Further, for example, in the DVB-S.2 standard, the parity check matrixH_(T) of the parity check matrix H=[H_(A)|H_(T)] has a staircasestructure.

It is necessary for the parity check matrix H and the row vector c=[A|T]as an LDPC code to satisfy the expression Hc^(T)=0, and where the paritymatrix H_(T) of the parity check matrix H=[H_(A)|H_(T)] has a staircasestructure, the row vector T as parity bits which configures the rowvector c=[A|T] which satisfies the expression Hc^(T)=0 can be determinedsequentially by setting the elements of each row to zero in orderbeginning with the elements in the first row of the column vector Hc^(T)in the expression Hc^(T)=0.

If the LDPC encoding section 21 determines a parity bit T for aninformation bit A, then it outputs a codeword c=[A|T] represented by theinformation bit A and the parity bit T as an LDPC encoding result of theinformation bit A.

As described above, the LDPC encoding section 21 stores the parity checkmatrix initial value tables corresponding to the code lengths N and theencoding rates r in advance therein and carries out LDPC encoding of theset code length N and the set encoding rate r using a parity checkmatrix H produced from the parity check matrix initial value tablescorresponding to the set code length N and the set encoding rate r.

Each parity check matrix initial value table is a table which representsthe position of elements of the value 1 of the information matrix H_(A)corresponding to the information length K corresponding to the codelength N and the encoding rate r of the LDPC code of the parity checkmatrix H (LDPC code defined by the parity check matrix H) for every 360rows (unit column number P of the periodic structure), and is producedin advance for a parity check matrix H for each code length N and eachencoding rate r.

FIGS. 78 to 123 illustrate the parity check matrix initial value tablesfor producing various parity check matrices H including parity checkmatrix initial value tables prescribed in the DVB-S.2 standard.

In particular, FIG. 78 shows the parity check matrix initial value tablefor a parity check matrix H prescribed in the DVB-S.2 standard andhaving a code length N of 16,200 bits and an encoding rate r of 2/3.

FIGS. 79 to 81 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 2/3.

It is to be noted that FIG. 80 is a view continuing from FIG. 79 andFIG. 81 is a view continuing from FIG. 80.

FIG. 82 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 3/4.

FIGS. 83 to 86 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 3/4.

It is to be noted that FIG. 84 is a view continuing from FIG. 83 andFIG. 85 is a view continuing from FIG. 84. Further, FIG. 86 is a viewcontinuing from FIG. 85.

FIG. 87 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 4/5.

FIGS. 88 to 91 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 4/5.

It is to be noted that FIG. 89 is a view continuing from FIG. 88 andFIG. 90 is a view continuing from FIG. 89. Further, FIG. 91 is a viewcontinuing from FIG. 90.

FIG. 92 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 5/6.

FIGS. 93 to 96 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 5/6.

It is to be noted that FIG. 94 is a view continuing from FIG. 93 andFIG. 95 is a view continuing from FIG. 94. Further, FIG. 96 is a viewcontinuing from FIG. 95.

FIG. 97 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 8/9.

FIGS. 98 to 101 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 8/9.

It is to be noted that FIG. 99 is a view continuing from FIG. 98 andFIG. 100 is a view continuing from FIG. 99. Further, FIG. 101 is a viewcontinuing from FIG. 100.

FIGS. 102 to 105 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 9/10.

It is to be noted that FIG. 103 is a view continuing from FIG. 102 andFIG. 104 is a view continuing from FIG. 103. Further, FIG. 105 is a viewcontinuing from FIG. 104.

FIGS. 106 and 107 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 1/4.

It is to be noted that FIG. 107 is a view continuing from FIG. 106.

FIGS. 108 and 109 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 1/3.

It is to be noted that FIG. 109 is a view continuing from FIG. 108.

FIGS. 110 and 111 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 2/5.

It is to be noted that FIG. 111 is a view continuing from FIG. 110.

FIGS. 112 to 114 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 1/2.

It is to be noted that FIG. 113 is a view continuing from FIG. 112 andFIG. 114 is a view continuing from FIG. 113.

FIGS. 115 to 117 show the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 64,800 bits and an encoding rate r of 3/5.

It is to be noted that FIG. 116 is a view continuing from FIG. 115 andFIG. 117 is a view continuing from FIG. 116.

FIG. 118 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 1/4.

FIG. 119 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 1/3.

FIG. 120 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 2/5.

FIG. 121 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 1/2.

FIG. 122 shows the parity check matrix initial value table for a paritycheck matrix H prescribed in the DVB-S.2 standard and having a codelength N of 16,200 bits and an encoding rate r of 3/5.

FIG. 123 shows the parity check matrix initial value table for a paritycheck matrix H having a code length N of 16,200 bits and an encodingrate r of 3/5, which can be used in place of the parity check matrixinitial value table of FIG. 122.

The LDPC encoding section 21 of the transmission apparatus 11 determinesa parity check matrix H in the following manner using the parity checkmatrix initial value tables.

In particular, FIG. 124 illustrates a method for determining a paritycheck matrix H from a parity check matrix initial value table.

It is to be noted that the parity check matrix initial value table ofFIG. 124 indicates the parity check matrix initial value table for aparity check matrix H prescribed in the DVB-S.2 standard and having acode length N of 16,200 bits and an encoding rate r of 2/3 shown in FIG.178.

As described above, the parity check matrix initial value table is atable which represents the position of elements of the value 1 of ainformation matrix H_(A) corresponding to the information length Kcorresponding to the code length N and the encoding rate r of the LDPCcode for every 360 columns (for every unit column number P of the cyclicstructure), and in the first row of the parity check matrix initialvalue table, a number of row numbers of elements of the value 1 in the1+360×(i−1)th column of the parity check matrix H (row numbers where therow number of the first row of the parity check matrix H is 0) equal tothe number of column weights which the 1+360×(i−1)th column has.

Here, it is assumed that the parity matrix H_(T) of the parity checkmatrix H corresponding to the parity length M has a staircase structureand is determined in advance. According to the parity check matrixinitial value table, the information matrix H_(A) corresponding to theinformation length K from within the parity check matrix H isdetermined.

The row number k+1 of the parity check matrix initial value tablediffers depending upon the information length K.

The information length K and the row number k+1 of the parity checkmatrix initial value table satisfy a relationship given by the followingexpression.K=(k+1)×360

Here, 360 in the expression above is the unit column number P of thecyclic structure.

In the parity check matrix initial value table of FIG. 124, 13 numericalvalues are listed in the first to third rows, and three numerical valuesare listed in the fourth to k+1th (in FIG. 124, 30th) rows.

Accordingly, the number of column weights in the parity check matrix Hdetermined from the parity check matrix initial value table of FIG. 124is 13 in the first to 1+360×(3−1)−1th rows but is 3 in the 1+360×(3−1)thto Kth rows.

The first row of the parity check matrix initial value table of FIG. 124includes 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451,4620 and 2622, and this indicates that, in the first column of theparity check matrix H, the elements in rows of the row numbers of 0,2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620 and2622 have the value 1 (and besides the other elements have the value 0).

Meanwhile, the second row of the parity check matrix initial value tableof FIG. 124 includes 1, 122, 1516, 3448, 2880, 1407, 1847, 3799, 3529,373, 971, 4358 and 3108, and this indicates that, in the 361st(=1+360×(2−1)th) column of the parity check matrix H, the elements inrows of the row numbers of 1, 122, 1546, 3448, 2880, 1407, 1847, 3799,3529, 373, 971, 4358 and 3108 have the value 1.

As given above, the parity check matrix initial value table representsthe position of elements of the value 1 of the information matrix H_(A)of the parity check matrix H for every 360 columns.

Each of the columns of the parity check matrix H other than the1+360×(i−1)th column, that is, each of the columns from 2+360×(i−1)th to360×ith columns, includes elements of the value of 1 obtained bycyclically shifting the elements of the value of 1 of the 1+360×(i−1)thcolumn which depend upon the parity check matrix initial value tableperiodically in the downward direction (in the downward direction of thecolumn) in accordance with the parity length M.

In particular, for example, the 2+360×(i−1)th column is a columnobtained by cyclically shifting the 1+360×(i−1)th column in the downwarddirection by M/360 (=q), and the next 3+360×(i−1)th is a column obtainedby cyclically shifting the 1+360×(i−1)th column in the downwarddirection by 2×M/360 (=2×q) and then cyclically shifting the cyclicallyshifted column (2+360×(i−1)th column) in the downward direction by M/360(=q).

Now, if it is assumed that the numeral value in the jth column (jth fromthe left) in the ith row (ith row from above) of the parity check matrixinitial value table is represented by b_(i), and the row number of thejth element of the value 1 in the wth column of the parity check matrixH is represented by H_(w-j), then the row number H_(w-j) of the elementof the value 1 in the wth column which is a column other than the1+360×(i−1)th column of the parity check matrix H can be determined inaccordance with the following expression.H _(w-j)=mod {h _(i,j)+mod((w−1),P)×q,M}

Here, mod(x,y) signifies a remainder when x is divided by y.

Meanwhile, P is a unit number of columns of the cyclic structuredescribed hereinabove and is, for example, in the DVB-S.2 standard, 360.Further, q is a value M/360 obtained by dividing the parity length M bythe unit column number P (=360) of the cyclic structure.

The LDPC encoding section 21 specifies the row number of the elements ofthe value 1 in the 1+360×(i−1)th column of the parity check matrix Hfrom the parity check matrix initial value table.

Further, the LDPC encoding section 21 determines the row number H_(w-j)of the element of the value 1 in the wth column which is a column otherthan the 1+360×(i−1)th column of the parity check matrix H and producesa parity check matrix H in which the elements of the row numbersobtained by the foregoing have the value 1.

Now, variations of the method of replacement of code bits of an LDPCcode in the replacement process by the replacement section 32 of thedemultiplexer 25 in the transmission apparatus 11, that is, of theallocation pattern (hereinafter referred to as bit allocation pattern)of code bits of an LDPC code and symbol bits representative of a symbol,are described.

In the demultiplexer 25, the code bits of the LDPC code are written inthe column direction of the memory 31, which stores (N/(mb))×(mb) bitsin the column direction×row direction. Thereafter, the code bits areread out in a unit of mb bits in the row direction. Further, in thedemultiplexer 25, the replacement section 32 replaces the mb code bitsread out in the row direction of the memory 31 and determines the codebits after the replacement as mb symbol bits of (successive) b symbols.

In particular, the replacement section 32 determines the i+1th bit fromthe most significant bit of the mb code bits read out in the rowdirection of the memory 31 as the code bit b_(i) and determines thei+1th bit from the most significant bit of the mb symbol bits of the b(successive) symbols as the symbol bit y_(i), and then replaces the mbcode bits b₀ to b_(mb-1) in accordance with a predetermined bitallocation pattern.

FIG. 125 shows an example of a bit allocation pattern which can beadopted where the LDPC code is an LDPC code whose code length N is64,800 bits and whose encoding rate is 5/6 or 9/10 and besides themodulation method is 4096QAM and the multiple b is 1.

Where the LDPC code is an LDPC code whose code length N is 64,800 bitsand whose encoding rate is 5/6 or 9/10 and besides the modulation methodis 4096QAM and the multiple b is 1, in the demultiplexer 25, the codebits written in the memory 31 for storing (64,800/(12×1))×(12×1) bits inthe column direction×row direction are read out in a unit of 12×1 (=mb)bits in the row direction and supplied to the replacement section 32.

The replacement section 32 replaces 12×1 (=mb) code bits b₀ to b₁₁ suchthat the 12×1 (=mb) code bits b₀ to b₁₁ to be read out from the memory31 may be allocated to the 12×1 (=mb) symbol bits y₀ to y₁₁ of one (=b)symbol as seen in FIG. 125.

In particular, according to FIG. 125, the replacement section 32 carriesout, with regard to both of an LDPC code having the encoding rate of 5/6and an LDPC code having the encoding rate of 9/10 from among LDPC codeshaving the code length N of 64,800 bits, replacement for allocating

the code bit b₀ to the symbol bit y₈,

the code bit b₁ to the symbol bit y₀,

the code bit b₂ to the symbol bit y₆,

the code bit b₃ to the symbol bit y₁,

the code bit b₄ to the symbol bit y₄,

the code bit b₅ to the symbol bit y₅,

the code bit b₆ to the symbol bit y₂,

the code bit b₇ to the symbol bit y₃,

the code bit b₈ to the symbol bit y₇,

the code bit b₉ to the symbol bit y₁₀,

the code bit b₁₀ to the symbol bit y₁₁, and

the code bit b₁₁ to the symbol bit y₉.

FIG. 226 shows an example of a bit allocation pattern which can beadopted where the LDPC code is an LDPC code whose code length N is64,800 bits and whose encoding rate is 5/6 or 9/10 and besides themodulation method is 4096QAM and the multiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 64,800 bitsand whose encoding rate is 5/6 or 9/10 and besides the modulation methodis 4096QAM and the multiple b is 2, in the demultiplexer 25, the codebits written in the memory 31 for storing (64,800/(12×2))×(12×2) bits inthe column direction×row direction are read out in a unit of 12×2 (=mb)bits in the row direction and supplied to the replacement section 32.

The replacement section 32 replaces 12×2 (=mb) code bits b₀ to b₂₃ suchthat the 12×2 (=mb) code bits b₀ to b₂₃ to be read out from the memory31 may be allocated to the 12×2 (=mb) symbol bits y₀ to y₂₃ of two (=b)successive symbols as seen in FIG. 126.

In particular, according to FIG. 126, the replacement section 32 carriesout, with regard to both of an LDPC code having the encoding rate of 5/6and an LDPC code having the encoding rate of 9/10 from among LDPC codeshaving the code length N of 64,800 bits, replacement for allocating

the code bit b₀ to the symbol bit y₈,

the code bit b₂ to the symbol bit y₀,

the code bit b₄ to the symbol bit y₆,

the code bit b₆ to the symbol bit y₁,

the code bit b₈ to the symbol bit y₄,

the code bit b₁₀ to the symbol bit y₅,

the code bit b₁₂ to the symbol bit y₂,

the code bit b₁₄ to the symbol bit y₃,

the code bit b₁₆ to the symbol bit y₇,

the code bit b₁₈ to the symbol bit y₁₀,

the code bit b₂₀ to the symbol bit y₁₁,

the code bit b₂₂ to the symbol bit y₉,

the code bit b₁ to the symbol bit y₂₀,

the code bit b₃ to the symbol bit y₁₂,

the code bit b₅ to the symbol bit y₁₈,

the code bit b₇ to the symbol bit y₁₃,

the code bit b₉ to the symbol bit y₁₆,

the code bit b₁₁ to the symbol bit y₁₇,

the code bit b₁₃ to the symbol bit y₁₄,

the code bit b₁₅ to the symbol bit y₁₅,

the code bit b₁₇ to the symbol bit y₁₉,

the code bit b₁₉ to the symbol bit y₂₂,

the code bit b₂₁ to the symbol bit y₂₃, and

the code bit b₂₃ to the symbol bit y₂₁.

Here, the bit allocation pattern of FIG. 126 utilizes the bit allocationpattern of FIG. 125 wherein the multiple b is 1 without anymodification. In particular, in FIG. 126, the allocation of the codebits b₀, b₂, . . . , b₂₂ to the symbol bits y_(i) and the allocation ofthe b₁, b₃, . . . , b₂₃ to the symbol bits y_(i) are similar to theallocation of the code bits b₀ to b₁₁ to the symbol bits y₁ of FIG. 125.

FIG. 127 shows an example of a bit allocation pattern which can beadopted where the modulation method is 1024QAM and the LDPC code is anLDPC code whose code length N is 16,200 bits and whose encoding rate is3/4, 5/6 or 8/9 and besides the multiple b is 2 and also where themodulation method is 1024QAM and the LDPC code is an LDPC code whosecode length N is 64,800 bits and whose encoding length is 3/4, 5/6 or9/10 and besides the multiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 16,200 bitsand whose encoding rate is 3/4, 5/6 or 8/9 and the modulation method is1024QAM and besides the multiple b is 2, in the demultiplexer 25, thecode bits written in the memory 31 for storing (16,200/(10×2))×(10×2)bits in the column direction×row direction are read out in a unit of10×2 (=mb) bits in the row direction and supplied to the replacementsection 32.

On the other hand, where the LDPC code is an LDPC code whose code lengthN is 64,800 bits and whose encoding rate is 3/4, 5/6 or 9/10 and themodulation method is 1024QAM and besides the multiple b is 2, in thedemultiplexer 25, the code bits written in the memory 31 for storing(64,800/(10×2))×(10×2) bits in the column direction×row direction areread out in a unit of 10×2 (=mb) bits in the row direction and suppliedto the replacement section 32.

The replacement section 32 replaces 10×2 (=mb) code bits b₀ to b₁₉ suchthat the 10×2 (=mb) code bits b₀ to b₁₉ to be read out from the memory31 may be allocated to the 10×2 (=mb) symbol bits y₀ to y₁₉ of two (=b)successive symbols as seen in FIG. 127.

In particular, according to FIG. 127, the replacement section 32 carriesout, with regard to all of the LDPC codes having the encoding rate of3/4, LDPC codes having the encoding rate of 5/6 and LDPC codes having afurther encoding rate of 8/9 from among LDPC codes having the codelength of 16,200 bits as well as LDPC code having the encoding rate of3/4, LDPC codes having the encoding rate of 5/6 and LDPC codes having afurther encoding rate of 9/10 from among LDPC codes having another codelength N of 64,800, replacement for allocating

the code bit b₀ to the symbol bit y₈,

the code bit b₁ to the symbol bit y₃,

the code bit b₂ to the symbol bit y₇,

the code bit b₃ to the symbol bit y₁₀,

the code bit b₄ to the symbol bit y₁₉,

the code bit b₅ to the symbol bit y₄,

the code bit b₆ to the symbol bit y₉,

the code bit b₇ to the symbol bit y₅,

the code bit b₈ to the symbol bit y₁₇,

the code bit b₉ to the symbol bit y₆,

the code bit b₁₀ to the symbol bit y₁₄,

the code bit b₁₁ to the symbol bit y₁₁,

the code bit b₁₂ to the symbol bit y₂,

the code bit b₁₃ to the symbol bit y₁₈,

the code bit b₁₄ to the symbol bit y₁₆,

the code bit b₁₅ to the symbol bit y₁₅,

the code bit b₁₆ to the symbol bit y₀,

the code bit b₁₇ to the symbol bit y₁,

the code bit b₁₈ to the symbol bit y₁₃, and

the code bit b₁₉ to the symbol bit y₁₂.

FIG. 128 shows an example of a bit allocation pattern which can beadopted where the modulation method is 4096QAM and the LDPC code is anLDPC code whose code length N is 16,200 bits and whose encoding rate is5/6 or 8/9 and besides the multiple b is 2 and also where the modulationmethod is 4096QAM and the LDPC code is an LDPC code whose code length Nis 64,800 bits and whose encoding rate is 5/6 or 9/10 and besides themultiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 16,200 bitsand whose encoding rate is 5/6 or 8/9 and the modulation method is4096QAM and besides the multiple b is 2, in the demultiplexer 25, thecode bits written in the memory 31 for storing (16,200/(12×2))×(12×2)bits in the column direction×row direction are read out in a unit of12×2 (=mb) bits in the row direction and supplied to the replacementsection 32.

On the other hand, where the LDPC code is an LDPC code whose code lengthN is 64,800 bits and whose encoding rate is 5/6 or 9/10 and themodulation method is 4096QAM and besides the multiple b is 2, in thedemultiplexer 25, the code bits written in the memory 31 for storing(64,800/(12×2))×(12×2) bits in the column direction×row direction areread out in a unit of 12×2 (=mb) bits in the row direction and suppliedto the replacement section 32.

The replacement section 32 replaces 12×2 (=mb) code bits b₀ to b₂₃ suchthat the 12×2 (=mb) bits to be read out from the memory 31 may beallocated to the 12×2 (=mb) symbol bits y₀ to y₂₃ of two (=b) successivesymbols as seen in FIG. 128.

In particular, according to FIG. 128, the replacement section 32 carriesout, with regard to all of the LDPC codes having the encoding rate of5/6 and LDPC codes having the encoding rate of 8/9 from among LDPC codeshaving the code length of 16,200 bits as well as LDPC codes having theencoding rate of 5/6 and LDPC codes having the encoding rate of 9/10from among LDPC codes having another code length N of 64,800,replacement for allocating

the code bit b₀ to the symbol bit y₁₀,

the code bit b₁ to the symbol bit y₁₅,

the code bit b₂ to the symbol bit y₄,

the code bit b₃ to the symbol bit y₁₉,

the code bit b₄ to the symbol bit y₂₁,

the code bit b₅ to the symbol bit y₁₆,

the code bit b₆ to the symbol bit y₂₃,

the code bit b₇ to the symbol bit y₁₈,

the code bit b₈ to the symbol bit y₁₁,

the code bit b₉ to the symbol bit y₁₄,

the code bit b₁₀ to the symbol bit y₂₂,

the code bit b₁₁ to the symbol bit y₅,

the code bit b₁₂ to the symbol bit y₆,

the code bit b₁₃ to the symbol bit y₁₇,

the code bit b₁₄ to the symbol bit y₁₃,

the code bit b₁₅ to the symbol bit y₂₀,

the code bit b₁₆ to the symbol bit y₁,

the code bit b₁₇ to the symbol bit y₃,

the code bit b₁₈ to the symbol bit y₉,

the code bit b₁₉ to the symbol bit y₂,

the code bit b₂₀ to the symbol bit y₇,

the code bit b₂₁ to the symbol bit y₈,

the code bit b₂₂ to the symbol bit y₁₂, and

the code bit y₂₃ to the symbol bit y₀.

According to the bit allocation patterns shown in FIGS. 125 to 128, thesame bit allocation pattern can be adopted for a plurality of kinds ofLDPC codes, and besides, the tolerance to errors can be set to a desiredperformance with regard to all of the plural kinds of LDPC codes.

In particular, FIGS. 129 to 132 illustrates results of simulations ofthe BER (Bit Error Rate) where a replacement process is carried out inaccordance with the bit allocation patterns of FIGS. 125 to 128.

It is to be noted that, in FIGS. 129 to 132, the axis of abscissarepresents E_(s)/N₀ (signal power to noise power ratio per one symbol)and the axis of ordinate represents the BER.

Further, a solid line curve represents the BER where a replacementprocess is carried out and an alternate long and short dash linerepresents the BER where a replacement process is not carried out.

FIG. 129 illustrates the BER where a replacement process in accordancewith the bit allocation pattern of FIG. 125 is carried out for LDPCcodes whose code length N is 64,800 and whose encoding rate is 5/6 and9/10 adopting 4096QAM as the modulation method and setting the multipleb to 1.

FIG. 130 illustrates the BER where a replacement process in accordancewith the bit allocation pattern of FIG. 126 is carried out for LDPCcodes whose code length N is 64,800 and whose encoding rate is 5/6 and9/10 adopting 4096QAM as the modulation method and setting the multipleb to 2.

It is to be noted that, in FIGS. 129 and 130, a graph having atriangular mark applied thereto represents the BER regarding the LDPCcode having the encoding rate of 5/6, and a graph having an asteriskapplied thereto represents the BER regarding the LDPC code having theencoding rate of 9/10.

FIG. 131 illustrates the BER where a replacement process in accordancewith the bit allocation pattern of FIG. 127 is carried out for LDPCcodes whose code length N is 16,200 and whose encoding rate is 3/4, 5/6and 8/9 and for LDPC codes whose code length N is 64,800 and whoseencoding rate is 3/4, 5/6 and 9/10 adopting 1024QAM as the modulationmethod and setting the multiple b to 2.

It is to be noted that, in FIG. 131, a graph having an asterisk appliedthereto represents the BER regarding the LDPC code having the codelength N of 64,800 and the encoding rate of 9/10, and a graph having anupwardly directed triangular mark applied thereto represents the BERregarding the LDPC codes having the code length N of 64,800 and theencoding rate of 5/6. Further, a graph having a square mark appliedthereto represents the BER regarding the LDPC code having the codelength N of 64,800 and the encoding rate of 3/4.

Further, in FIG. 131, a graph having a round mark applied theretorepresents the BER regarding the LDPC code having the code length N of16,200 and the encoding rate of 8/9, and a graph having a downwardlydirected triangular mark applied thereto represents the BER regardingthe LDPC code having the code length N of 16,200 and the encoding rateof 5/6. Further, a graph having a plus mark applied thereto representsthe BER regarding the LDPC code having the code length N of 16,200 andthe encoding rate of 3/4.

FIG. 132 illustrates the BER where a replacement process in accordancewith the bit allocation pattern of FIG. 128 is carried out for LDPCcodes whose code length N is 16,200 and whose encoding rate is 5/6 and8/9 and for LDPC codes whose code length N is 64,800 and whose encodingrate is 5/6 and 9/10 adopting 4096QAM as the modulation method andsetting the multiple b to 2.

It is to be noted that, in FIG. 132, a graph having an asterisk appliedthereto represents the BER regarding the LDPC code having the codelength N of 64,800 and the encoding rate of 9/10, and a graph having anupwardly directed triangular mark applied thereto represents the BERregarding the LDPC codes having the code length N of 64,800 and theencoding rate of 5/6.

Further, in FIG. 132, a graph having a round mark applied theretorepresents the BER regarding the LDPC code having the code length N of16,200 and the encoding rate of 8/9, and a graph having a downwardlydirected triangular mark applied thereto represents the BER regardingthe LDPC code having the code length N of 16,200 and the encoding rateof 5/6.

According to FIGS. 129 to 132, the same bit allocation pattern can beadopted with regard to a plurality of kinds of LDPC codes. Besides, thetolerance to errors can be set to a desired performance with regard toall of the plural kinds of LDPC codes.

In particular, where a bit allocation pattern for exclusive use isadopted for each of a plurality of kinds of LDPC codes which havedifferent code lengths and different encoding rates, the tolerance to anerror can be raised to a very high performance. However, it is necessaryto change the bit allocation pattern for each of a plurality of kinds ofLDPC codes.

On the other hand, according to the bit allocation patterns of FIGS. 125to 128, the same bit allocation pattern can be adopted for a pluralityof kinds of LDPC codes which have different code lengths and differentencoding rates, and the necessity to change the bit allocation patternfor each of a plurality of kinds of LDPC codes as in a case wherein abit allocation pattern for exclusive use is adopted for each of aplurality of kinds of LDPC codes is eliminated.

Further, according to the bit allocation patterns of FIGS. 125 to 128,the tolerance to errors can be raised to a high performance although itis a little lower than that where a bit allocation pattern for exclusiveuse is adopted for each of a plurality of kinds of LDPC codes.

In particular, for example, where the modulation method is 4096QAM, thesame bit allocation pattern in FIG. 125 or 126 can be used for all ofthe LDPC codes which have the code length N of 64,800 and the encodingrate of 5/6 and 9/10. Even where the same bit allocation pattern isadopted in this manner, the tolerance to errors can be raised to a highperformance.

Further, for example, where the modulation method is 1024QAM, the samebit allocation pattern of FIG. 127 can be adopted for all of the LDPCcodes which have the code length N of 16,200 and the encoding rate of3/4, 5/6 and 8/9 and the LDPC codes which have the code length N of64,800 and the encoding rate of 3/4, 5/6 and 9/10. Then, even if thesame bit allocation pattern is adopted in this manner, the tolerance toerrors can be raised to a high performance.

Meanwhile, for example, where the modulation method is 4096QAM, the samebit allocation pattern of FIG. 128 can be adopted for all of the LDPCcodes which have the code length N of 16,200 and the encoding rate of5/6 and 8/9 and the LDPC codes which have the code length N of 64,800and the encoding rate of 5/6 and 9/10. Then, even if the same bitallocation pattern is adopted in this manner, the tolerance to errorscan be raised to a high performance.

Variations of the bit allocation pattern are further described.

FIG. 133 illustrates an example of a bit allocation pattern which can beadopted where the LDPC code is any LDPC code which has the code length Nof 16,200 or 64,800 bits and one of the encoding rates for the LDPC codedefined by a parity check matrix H produced, for example, from any ofthe parity check matrix initial value tables shown in FIGS. 78 to 123other than the encoding rate of 3/5 and besides the modulation method isQPSK and the multiple b is 1.

Where the LDPC code is an LDPC code which has the code length N of16,200 or 64,800 bits and has the encoding rate other than 3/5 andbesides the modulation method is QPSK and the multiple b is 1, thedemultiplexer 25 reads out code bits written in the memory 31 forstoring (N/(2×1))×(2×1) bits in the column direction×row direction in aunit of 2×1 (=mb) bits in the row direction and supplies the read outcode bits to the replacement section 32.

The replacement section 32 replaces the 2×1 (=mb) code bits b₀ and b₁read out from the memory 31 in such a manner that the 2×1 (=mb) codebits b₀ and b₁ are allocated to the 2×1 (=mb) symbol bits y₀ and y₁ ofone (=b) symbol as seen in FIG. 133.

In particular, according to FIG. 133, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₀ and

the code bit b₁ to the symbol bit y₁.

It is to be noted that, in this instance, also it is possible toconsider that replacement is not carried out and the code bits b₀ and b₁are determined as they are as the symbol bits y₀ and y₁, respectively.

FIG. 134 shows an example of a bit allocation pattern which can beadopted where the LDPC code is an LDPC code which has the code length Nof 16,200 or 64,800 bits and has the encoding rate other than 3/5 andbesides the modulation method is 16QAM and the multiple b is 2.

Where the LDPC code is an LDPC code which has the code length N of16,200 or 64,800 bits and has the encoding rate other than 3/5 andbesides the modulation method is 16QAM and the multiple b is 2, thedemultiplexer 25 reads out the code bits written in the memory 31 forstoring (N/(4×2))×(4×2) bits in the column direction×row direction in aunit of 4×2 (=mb) bits in the row direction and supplies the read outcode bits to the replacement section 32.

The replacement section 32 replaces the 4×2 (=mb) code bits b₀ to b₇read out from the memory 31 in such a manner that the 4×2 (=mb) codebits are allocated to the 4×2 (=mb) symbol bits y₀ to y₇ of two (=b)successive symbols as seen in FIG. 134.

In particular, according to FIG. 134, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₇,

the code bit b₁ to the symbol bit y₁,

the code bit b₂ to the symbol bit y₄,

the code bit b₃ to the symbol bit y₂,

the code bit b₄ to the symbol bit y₅,

the code bit b₅ to the symbol bit y₃,

the code bit b₆ to the symbol bit y₆, and

the code bit b₇ to the symbol bit y₀.

FIG. 135 shows an example of a bit allocation pattern which can beadopted where the modulation method is 64QAM and the LDPC code is anLDPC code whose code length N is 16,200 or 64,800 bits and whoseencoding rate is any other than 3/5 and besides the multiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 16,200 or64,800 bits and whose encoding rate is any other than 3/5 and themodulation method is 64QAM and besides the multiple b is 2, in thedemultiplexer 25, the code bits written in the memory 31 for storing(N/(6×2))×(6×2) bits in the column direction×row direction are read outin a unit of 6×2 (=mb) bits in the row direction and supplied to thereplacement section 32.

The replacement section 32 replaces the 6×2 (=mb) code bits b₀ to b₁₁read out from the memory 31 such that the 6×2 (=mb) code bits b₀ to b₁₁may be allocated to the 6×2 (=mb) symbol bits y₀ to y₁₁ of two (=b)successive symbols as seen in FIG. 135.

In particular, according to FIG. 135, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₁₁,

the code bit b₁ to the symbol bit y₇,

the code bit b₂ to the symbol bit y₃,

the code bit b₃ to the symbol bit y₁₀,

the code bit b₄ to the symbol bit y₆,

the code bit b₅ to the symbol bit y₂,

the code bit b₆ to the symbol bit y₉,

the code bit b₇ to the symbol bit y₅,

the code bit b₈ to the symbol bit y₁,

the code bit b₉ to the symbol bit y₈,

the code bit b₁₀ to the symbol bit y₄, and

the code bit b₁₁ to the symbol bit y₀.

FIG. 136 shows an example of a bit allocation pattern which can beadopted where the modulation method is 256QAM and the LDPC code is anLDPC code whose code length N is 64,800 bits and whose encoding rate isany other than 3/5 and besides the multiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 64,800 bitsand whose encoding rate is any other than 3/5 and the modulation methodis 256QAM and besides the multiple b is 2, in the demultiplexer 25, thecode bits written in the memory 31 for storing (64,800/(8×2))×(8×2) bitsin the column direction×row direction are read out in a unit of 8×2(=mb) bits in the row direction and supplied to the replacement section32.

The replacement section 32 replaces the 8×2 (=mb) code bits b₀ to b₁₅read out from the memory 31 such that the 8×2 (=mb) code bits b₀ to b₁₅may be allocated to the 8×2 (=mb) symbol bits y₀ to y₁₅ of two (=b)successive symbols as seen in FIG. 136.

In particular, according to FIG. 136, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₁₅,

the code bit b₁ to the symbol bit y₁,

the code bit b₂ to the symbol bit y₁₃,

the code bit b₃ to the symbol bit y₃,

the code bit b₄ to the symbol bit y₈,

the code bit b₅ to the symbol bit y₁₁,

the code bit b₆ to the symbol bit y₉,

the code bit b₇ to the symbol bit y₅,

the code bit b₈ to the symbol bit y₁₀,

the code bit b₉ to the symbol bit y₆,

the code bit b₁₀ to the symbol bit y₄,

the code bit b₁₁ to the symbol bit y₇,

the code bit b₁₂ to the symbol bit y₁₂,

the code bit b₁₃ to the symbol bit y₂,

the code bit b₁₄ to the symbol bit y₁₄, and

the code bit b₁₅ to the symbol bit y₀.

FIG. 137 shows an example of a bit allocation pattern which can beadopted where the modulation method is 256QAM and the LDPC code is anLDPC code whose code length N is 16,200 bits and whose encoding rate isany other than 3/5 and besides the multiple b is 1.

Where the LDPC code is an LDPC code whose code length N is 16,200 bitsand whose encoding rate is any other than 3/5 and the modulation methodis 256QAM and besides the multiple b is 1, in the demultiplexer 25, thecode bits written in the memory 31 for storing (16,200/(8×1))×(8×1) bitsin the column direction×row direction are read out in a unit of 8×1(=mb) bits in the row direction and supplied to the replacement section32.

The replacement section 32 replaces the 8×1 (=mb) code bits b₀ to b₂read out from the memory 31 such that the 8×1 (=mb) code bits b₀ to b₂may be allocated to the 8×1 (=mb) symbol bits y₀ to y₂ of one (=b)symbol as seen in FIG. 137.

In particular, according to FIG. 137, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₇,

the code bit b₁ to the symbol bit y₃,

the code bit b₂ to the symbol bit y₁,

the code bit b₃ to the symbol bit y₅,

the code bit b₄ to the symbol bit y₂,

the code bit b₅ to the symbol bit y₆,

the code bit b₆ to the symbol bit y₄, and

the code bit b₇ to the symbol bit y₀.

FIG. 138 shows an example of a bit allocation pattern which can beadopted where the LDPC code is an LDPC code whose code length N is16,200 or 64,800 bits and whose encoding rate is any other than 3/5 andbesides the modulation method is QPSK and the multiple b is 1.

Where the LDPC code is an LDPC code whose code length N is 16,200 or64,800 bits and whose encoding rate is any other than 3/5 and besidesthe modulation method is QPSK and the multiple b is 1, in thedemultiplexer 25, the code bits written in the memory 31 for storing(N/(2×1))×(2×1) bits in the column direction×row direction are read outin a unit of 2×1 (=mb) bits in the row direction and supplied to thereplacement section 32.

The replacement section 32 replaces the 2×1 (=mb) code bits b₀ and b₁read out from the memory 31 such that the 2×1 (=mb) code bits b₀ and b₁may be allocated to the 2×1 (=mb) symbol bits y₀ and y₁ of one (=b)symbol as seen in FIG. 138.

In particular, according to FIG. 138, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₀, and

the code bit b₁ to the symbol bit y₂.

It is to be noted that, in this instance, also it is possible toconsider that replacement is not carried out and the code bits b₀ and b₁are determined as they are as the symbol bits y₀ and y₁, respectively.

FIG. 139 shows an example of a bit allocation pattern which can beadopted where the LDPC code is an LDPC code whose code length N is64,800 bits and whose encoding rate is 3/5 and besides the modulationmethod is 16QAM and the multiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 64,800 bitsand whose encoding rate is 3/5 and besides the modulation method is16QAM and the multiple b is 2, in the demultiplexer 25, the code bitswritten in the memory 31 for storing (64,800/(4×2))×(4×2) bits in thecolumn direction×row direction are read out in a unit of 4×2 (=mb) bitsin the row direction and supplied to the replacement section 32.

The replacement section 32 replaces the 4×2 (=mb) code bits b₀ to b₇read out from the memory 31 such that the 4×2 (=mb) code bits b₀ to b₇may be allocated to the 4×2 (=mb) symbol bits y₀ to y₇ of two (=b)successive symbols as seen in FIG. 139.

In particular, according to FIG. 139, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₀,

the code bit b₁ to the symbol bit y₅,

the code bit b₂ to the symbol bit y₁,

the code bit b₃ to the symbol bit y₂,

the code bit b₄ to the symbol bit y₄,

the code bit b₅ to the symbol bit y₇,

the code bit b₆ to the symbol bit y₃, and

the code bit b₇ to the symbol bit y₆.

FIG. 140 shows an example of a bit allocation pattern which can beadopted where the LDPC code is an LDPC code whose code length N is16,200 bits and whose encoding rate is 3/5 and besides the modulationmethod is 16QAM and the multiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 16,200 bitsand whose encoding rate is 3/5 and besides the modulation method is16QAM and the multiple b is 2, in the demultiplexer 25, the code bitswritten in the memory 31 for storing (16,200/(4×2))×(4×2) bits in thecolumn direction×row direction are read out in a unit of 4×2 (=mb) bitsin the row direction and supplied to the replacement section 32.

The replacement section 32 replaces the 4×2 (=mb) code bits b₀ to b₇read out from the memory 31 such that the 4×2 (=mb) code bits b₀ to b₂may be allocated to the 4×2 (=mb) symbol bits y₀ to y₇ of two (=b)successive symbols as seen in FIG. 240.

In particular, according to FIG. 140, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₇,

the code bit b₁ to the symbol bit y₁,

the code bit b₂ to the symbol bit y₄,

the code bit b₃ to the symbol bit y₂,

the code bit b₄ to the symbol bit y₅,

the code bit b₅ to the symbol bit y₃,

the code bit b₆ to the symbol bit y₆, and

the code bit b₇ to the symbol bit y₀.

FIG. 141 shows an example of a bit allocation pattern which can beadopted where the modulation method is 64QAM and the LDPC code is anLDPC code whose code length N is 64,800 bits and whose encoding rate is3/5 and besides the multiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 64,800 bitsand whose encoding rate is 3/5 and the modulation method is 64QAM andbesides the multiple b is 2, in the demultiplexer 25, the code bitswritten in the memory 31 for storing (64,800/(6×2))×(6×2) bits in thecolumn direction×row direction are read out in a unit of 6×2 (=mb) bitsin the row direction and supplied to the replacement section 32.

The replacement section 32 replaces the 6×2 (=mb) code bits b₀ to b₁₁read out from the memory 31 such that the 6×2 (=mb) code bits b₀ to b₁₁may be allocated to the 6×2 (=mb) symbol bits y₀ to y₁₁ of two (=b)successive symbols as seen in FIG. 141.

In particular, according to FIG. 141, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₂,

the code bit b₁ to the symbol bit y₇,

the code bit b₂ to the symbol bit y₆,

the code bit b₃ to the symbol bit y₉,

the code bit b₄ to the symbol bit y₀,

the code bit b₅ to the symbol bit y₃,

the code bit b₆ to the symbol bit y₁,

the code bit b₇ to the symbol bit y₈,

the code bit b₈ to the symbol bit y₄,

the code bit b₉ to the symbol bit y₁₁,

the code bit b₁₀ to the symbol bit y₅, and

the code bit b₁₁ to the symbol bit y₁₀.

FIG. 142 shows an example of a bit allocation pattern which can beadopted where the modulation method is 64QAM and the LDPC code is anLDPC code whose code length N is 16,200 bits and whose encoding rate is3/5 and besides the multiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 16,200 bitsand whose encoding rate is 3/5 and the modulation method is 64QAM andbesides the multiple b is 2, in the demultiplexer 25, the code bitswritten in the memory 31 for storing (16,200/(6×2))×(6×2) bits in thecolumn direction×row direction are read out in a unit of 6×2 (=mb) bitsin the row direction and supplied to the replacement section 32.

The replacement section 32 replaces the 6×2 (=mb) code bits b₀ to b₁₁read out from the memory 31 such that the 6×2 (=mb) code bits b₀ to b₁₁may be allocated to the 6×2 (=mb) symbol bits y₀ to y₁₁ of two (=b)successive symbols as seen in FIG. 142.

In particular, according to FIG. 142, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₁₁,

the code bit b₁ to the symbol bit y₇,

the code bit b₂ to the symbol bit y₃,

the code bit b₃ to the symbol bit y₁₀,

the code bit b₄ to the symbol bit y₆,

the code bit b₅ to the symbol bit y₂,

the code bit b₆ to the symbol bit y₉,

the code bit b₇ to the symbol bit y₅,

the code bit b₈ to the symbol bit y₁,

the code bit b₉ to the symbol bit y₈,

the code bit b₁₀ to the symbol bit y₄, and

the code bit b₁₁ to the symbol bit y₀.

FIG. 143 shows an example of a bit allocation pattern which can beadopted where the modulation method is 256QAM and the LDPC code is anLDPC code whose code length N is 64,800 bits and whose encoding rate is3/5 and besides the multiple b is 2.

Where the LDPC code is an LDPC code whose code length N is 64,800 bitsand whose encoding rate is 3/5 and the modulation method is 256QAM andbesides the multiple b is 2, in the demultiplexer 25, the code bitswritten in the memory 31 for storing (64,800/(8×2))×(8×2) bits in thecolumn direction×row direction are read out in a unit of 8×2 (=mb) bitsin the row direction and supplied to the replacement section 32.

The replacement section 32 replaces the 8×2 (=mb) code bits b₀ to b₁₅read out from the memory 31 such that the 8×2 (=mb) code bits b₀ to b₁₅may be allocated to the 8×2 (=mb) symbol bits y₀ to y₁₅ of two (=b)successive symbols as seen in FIG. 143.

In particular, according to FIG. 143, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₂,

the code bit b₁ to the symbol bit y₁₁,

the code bit b₂ to the symbol bit y₃,

the code bit b₃ to the symbol bit y₄,

the code bit b₄ to the symbol bit y₀,

the code bit b₅ to the symbol bit y₉,

the code bit b₆ to the symbol bit y₁,

the code bit b₇ to the symbol bit y₈,

the code bit b₈ to the symbol bit y₁₀,

the code bit b₉ to the symbol bit y₁₃,

the code bit b₁₀ to the symbol bit y₇,

the code bit b₁₁ to the symbol bit y₁₄,

the code bit b₁₂ to the symbol bit y₆,

the code bit b₁₃ to the symbol bit y₁₅,

the code bit b₁₄ to the symbol bit y₅, and

the code bit b₁₅ to the symbol bit y₁₂.

FIG. 144 shows an example of a bit allocation pattern which can beadopted where the modulation method is 256QAM and the LDPC code is anLDPC code whose code length N is 16,200 bits and whose encoding rate is3/5 and besides the multiple b is 1.

Where the LDPC code is an LDPC code whose code length N is 16,200 bitsand whose encoding rate is 3/5 and the modulation method is 256QAM andbesides the multiple b is 1, in the demultiplexer 25, the code bitswritten in the memory 31 for storing (16,200/(8×1))×(8×1) bits in thecolumn direction×row direction are read out in a unit of 8×1 (=mb) bitsin the row direction and supplied to the replacement section 32.

The replacement section 32 replaces the 8×1 (=mb) code bits b₀ to b₇read out from the memory 31 such that the 8×1 (=mb) code bits b₀ to b₇may be allocated to the 8×1 (=mb) symbol bits y₀ to y₇ of one (=b)symbol as seen in FIG. 144.

In particular, according to FIG. 144, the replacement section 32 carriesout replacement for allocating

the code bit b₀ to the symbol bit y₇,

the code bit b₁ to the symbol bit y₃,

the code bit b₂ to the symbol bit y₁,

the code bit b₃ to the symbol bit y₅,

the code bit b₄ to the symbol bit y₂,

the code bit b₅ to the symbol bit y₆,

the code bit b₆ to the symbol bit y₄, and

the code bit b₇ to the symbol bit y₀.

Now, the deinterleaver 53 which composes the reception apparatus 12 isdescribed.

FIG. 145 is a view illustrating processing of the multiplexer 54 whichcomposes the deinterleaver 53.

In particular, FIG. 145A shows an example of a functional configurationof the multiplexer 54.

The multiplexer 54 is composed of a reverse replacement section 1001 anda memory 1002.

The multiplexer 54 determines symbol bits of symbols supplied from thedemapping section 52 at the preceding stage as an object of processingthereof and carries out a reverse replacement process corresponding tothe replacement process carried out by the demultiplexer 25 of thetransmission apparatus 11 (process reverse to the replacement process),that is, a reverse replacement process of returning the positions of thecode bits (symbol bits) of the LDPC code replaced by the replacementprocess. Then, the multiplexer 54 supplies an LDPC code obtained as aresult of the reverse replacement process to the column twistdeinterleaver 55 at the succeeding stage.

In particular, in the multiplexer 54, mb symbol bits y₀, y₁, . . . ,y_(mb-1) of b symbols are supplied in a unit of b (successive) symbolsto the reverse replacement section 1001.

The reverse replacement section 1001 carries out reverse replacement ofreturning the arrangement of the mb symbol bits y₀ to y_(mb-1) to theoriginal arrangement of the mb code bits b₀, b₁, . . . , b_(mb-1)(arrangement of the code bits b₀ to b_(mb-1) before the replacement bythe replacement section 32 which composes the demultiplexer 25 on thetransmission apparatus 11 side is carried out). The reverse replacementsection 1001 outputs code bits b₀ to b_(mb-1) obtained as a result ofthe reverse replacement.

The memory 1002 has a storage capacity of storing mb bits in the row(horizontal) direction and storing N/(mb) bits in the column (vertical)direction similarly to the memory 31 which composes the demultiplexer 25of the transmission apparatus 11 side. In other words, the reversereplacement section 1001 is configured from mb columns each of whichstores N/(mb) bits.

However, in the memory 1002, writing of the code bits of LDPC codesoutputted from the reverse replacement section 1001 is carried out in adirection in which reading out of code bits from the memory 31 of thedemultiplexer 25 of the transmission apparatus 11 is carried out, andreading out of code bits written in the memory 1002 is carried out in adirection in which writing of code bits into the memory 31 is carriedout.

In particular, the multiplexer 54 of the reception apparatus 12successively carries out writing of code bits of an LDPC code outputtedfrom the reverse replacement section 1001 in a unit of mb bits in therow direction beginning with the first row of the memory 1002 toward alower low as seen in FIG. 145A.

Then, when the writing of code bits for one code length ends, themultiplexer 54 reads out the code bits in the column direction from thememory 1002 and supplies the code bits to the column twist deinterleaver55 at the succeeding stage.

Here, FIG. 145B is a view illustrating reading out of the code bits fromthe memory 1002.

The multiplexer 54 carries out reading out of code bits of an LDPC codein a downward direction (column direction) from above of a column whichcomposes the memory 1002 beginning with a leftmost column toward a rightside column.

Now, processing of the column twist deinterleaver 55 which composes thedeinterleaver 53 of the reception apparatus 12 is described withreference to FIG. 146.

FIG. 146 shows an example of a configuration of the memory 1002 of themultiplexer 54.

The memory 1002 has a storage capacity for storing mb bits in the column(vertical) direction and stores N/(mb) bits in the row (horizontal)direction and is composed of mb columns.

The column twist deinterleaver 55 writes code bits of an LDPC code inthe row direction into the memory 1002 and controls the position atwhich reading out is started when the code bits are read out in thecolumn direction to carry out column twist deinterleave.

In particular, the column twist deinterleaver 55 carries out a reversere-arrangement process of suitably changing the reading out startingposition at which reading out of code bits with regard to each of aplurality of columns is to be started to return the arrangement of codebits re-arranged by the column twist interleave to the originalarrangement.

Here, FIG. 146 shows an example of a configuration of the memory 1002where the modulation method is 16QAM and the multiple b is 1.Accordingly, the bit number m of one symbol is 4 bits, and the memory1002 includes four (=mb) columns.

The column twist deinterleaver 55 carries out (in place of themultiplexer 54), writing of code bits of an LDPC code outputted from thereplacement section 1001 in the row direction successively into thememory 1002 beginning with the first row toward a lowermost row.

Then, if writing of code bits for one code length ends, then the columntwist deinterleaver 55 carries out reading out of code bits in thedownward direction (column direction) from a top of the memory 1002beginning with a leftmost column toward a right side column.

However, the column twist deinterleaver 55 carries out reading out ofthe code bits from the memory 1002 determining the writing startingposition upon writing of the code bits by the column twist interleaver24 on the transmission apparatus 11 side to a reading out startingposition of the code bits.

In particular, if the address of the position of the top of each columnis determined as 0 and the address of each position in the columndirection is represented by an integer given in an ascending order, thenwhere the modulation method is 16QAM and the multiple b is 1, the columntwist deinterleaver 55 sets the reading out starting position for theleftmost column to the position whose address is 0, sets the reading outstarting position for the second column (from the left) to the positionwhose address is 2, sets the reading out starting position for the thirdcolumn to the position whose address is 4, and sets the reading outstarting position for the fourth column to the position whose address is7.

It is to be noted that, with regard to each of those columns whosereading out starting position has an address other than 0, reading outof code bits is carried out such that, after such reading out is carriedout down to the lowermost position, the reading out position is returnedto the top (position whose address is 0) of the column and the readingout is carried out downwardly to the position immediately preceding tothe reading out starting position. Then, after that, reading out iscarried out from the next (right) column.

By carrying out such column twist interleave as described above, thearrangement of the code bits re-arranged by the column twist interleaveis returned to the original arrangement.

FIG. 147 is a block diagram showing another example of the configurationof the reception apparatus 12.

Referring to FIG. 147, the reception apparatus 12 is a data processingapparatus which receives a modulation signal from the transmissionapparatus 11 and includes an orthogonal demodulation section 51, ademapping section 52, a deinterleaver 53 and an LDPC decoding section1021.

The orthogonal demodulation section 51 receives a modulation signal fromthe transmission apparatus 11, carries out orthogonal demodulation andsupplies symbols (values in the I and Q axis directions) obtained as aresult of the orthogonal demodulation to the demapping section 52.

The demapping section 52 carries out demapping of converting the symbolsfrom the orthogonal demodulation section 51 into code bits of an LDPCcode and supplies the code bits to the deinterleaver 53.

The deinterleaver 53 includes a multiplexer (MUX) 54, a column twistdeinterleaver 55 and a parity deinterleaver 1011 and carries outdeinterleave of the code bits of the LDPC code from the demappingsection 52.

In particular, the multiplexer 54 determines an LDPC code from thedemapping section 52 as an object of processing thereof and carries outa reverse replacement process corresponding to the replacement processcarried out by the demultiplexer 25 of the transmission apparatus(reverse process to the replacement process), that is, a reversereplacement process of returning the positions of the code bits replacedby the replacement process to the original positions. Then, themultiplexer 54 supplies an LDPC code obtained as a result of the reversereplacement process to the column twist deinterleaver 55.

The column twist deinterleaver 55 determines the LDPC code from themultiplexer 54 as an object of processing and carries out column twistdeinterleave corresponding to the column twist interleave as are-arrangement process carried out by the column twist interleaver 24 ofthe transmission apparatus 11.

The LDPC code obtained as a result of the column twist deinterleave issupplied from the column twist deinterleaver 55 to the paritydeinterleaver 1011.

The parity deinterleaver 1011 determines the code bits after the columntwist deinterleave by the column twist deinterleaver 55 as an object ofprocessing thereof and carries out parity deinterleave corresponding tothe parity interleave carried out by the parity interleaver 23 of thetransmission apparatus 11 (reverse process to the parity interleave),that is, parity deinterleave of returning the arrangement of the codebits of the LDPC code whose arrangement was changed by the parityinterleave to the original arrangement.

The LDPC code obtained as a result of the parity deinterleave issupplied from the parity deinterleaver 1011 to the LDPC decoding section1021.

Accordingly, in the reception apparatus 12 of FIG. 147, the LDPC codefor which the reverse replacement process, column twist deinterleave andparity deinterleave have been carried out, that is, an LDPC codeobtained by LDPC coding in accordance with the parity check matrix H, issupplied to the LDPC decoding section 1021.

The LDPC decoding section 1021 carries out LDPC decoding of the LDPCcode from the deinterleaver 53 using the parity check matrix H itselfused for LDPC encoding by the LDPC encoding section 21 of thetransmission apparatus 11 or a conversion parity check matrix obtainedby carrying out at least column conversion corresponding to the parityinterleave for the parity check matrix H. Then, the LDPC decodingsection 1021 outputs data obtained by the LDPC decoding as a decodingresult of the object data.

Here, in the reception apparatus 12 of FIG. 147, since an LDPC codeobtained by LDPC encoding in accordance with the parity check matrix His supplied from the (parity deinterleaver 1011 of) the deinterleaver 53to the LDPC decoding section 1021, where the LDPC decoding of the LDPCcode is carried out using the parity check matrix H itself used for theLDPC encoding by the LDPC encoding section 21 of the transmissionapparatus 11, the LDPC decoding section 1021 can be configured, forexample, from a decoding apparatus which carries out LDPC decoding inaccordance with a full serial decoding method wherein mathematicaloperation of messages (check node messages and variable node messages)is carried out for one by one node or another decoding apparatus whereinLDPC decoding is carried out in accordance with a full parallel decodingmethod wherein mathematical operation of messages are carried outsimultaneously (in parallel) for all nodes.

Further, where LDPC decoding of an LDPC code is carried out using aconversion parity check matrix obtained by carrying out at least columnreplacement corresponding to the parity interleave for the parity checkmatrix H used in the LDPC encoding by the LDPC encoding section 21 ofthe transmission apparatus 11, the LDPC decoding section 1021 can beconfirmed from a decoding apparatus of an architecture which carries outthe check node mathematical operation and the variable node mathematicaloperation simultaneously for P (or a devisor of P other than 1) checknodes and P variable nodes and which has a reception data re-arrangementsection 310 for carrying out column replacement similar to the columnreplacement for obtaining a conversion parity check matrix for the LDPCcode to re-arrange the code bits of the LDPC codes.

It is to be noted that, while, in FIG. 147, the multiplexer 54 forcarrying out the reverse replacement process, column twist deinterleaver55 for carrying out the column twist deinterleave and paritydeinterleaver 1011 for carrying out the parity deinterleave areconfigured separately from each other for the convenience ofdescription, two or more of the multiplexer 54, column twistdeinterleaver 55 and parity deinterleaver 1011 can be configuredintegrally similarly to the parity interleaver 23, column twistinterleaver 24 and demultiplexer 25 of the transmission apparatus 11.

FIG. 148 is a block diagram showing a first example of a configurationof a reception system which can be applied to the reception apparatus12.

Referring to FIG. 148, the reception system includes an acquisitionsection 1101, a transmission line decoding processing section 1102 andan information source decoding processing section 1103.

The acquisition section 1101 acquires a signal including an LDPC codeobtained at least by LDPC encoding object data such as image data andmusic data of a program through a transmission line such as, forexample, terrestrial digital broadcasting, satellite digitalbroadcasting, a CATV network, the Internet or some other network. Then,the acquisition section 1101 supplies the acquired signal to thetransmission line decoding processing section 1102.

Here, where the signal acquired by the acquisition section 1101 isbroadcast, for example, from a broadcasting station through groundwaves, satellite waves, a CATV (Cable Television) or the like, theacquisition section 1101 is configured from a tuner, an STB (Set TopBox) or the like. On the other hand, where the signal acquired by theacquisition section 1101 is transmitted in a multicast state as in theIPTV (Internet Protocol Television), for example, from a web server, theacquisition section 11 is configured from a network I/F (Inter face)such as, for example, an NIC (Network Interface Card).

The transmission line decoding processing section 1102 carries out atransmission line decoding process including at least a process forcorrecting errors produced in the transmission line for the signalacquired through the transmission line by the acquisition section 1101,and supplies a signal obtained as a result of the transmission linedecoding process to the information source decoding processing section1103.

In particular, the signal acquired through the transmission line by theacquisition section 1101 is a signal obtained by carrying out at leasterror correction encoding for correcting errors produced in thetransmission line, and for such a signal as just described, thetransmission line decoding processing section 1102 carries out atransmission line decoding process such as, for example, an errorcorrection process.

Here, as the error correction encoding, for example, LDPC encoding,Reed-Solomon encoding and so forth are available. Here, as the errorcorrection encoding, at least LDPC encoding is carried out.

Further, the transmission line decoding process sometimes includesdemodulation of a modulation signal and so forth.

The information source decoding processing section 1103 carries out aninformation source decoding process including at least a process fordecompressing compressed information into original information for thesignal for which the transmission line decoding process has been carriedout.

In particular, the signal acquired through the transmission line by theacquisition section 1101 has sometimes been processed by compressionencoding for compressing information in order to reduce the data amountsuch as images, sound and so forth as information. In this instance, theinformation source decoding processing section 1103 carries out aninformation source decoding process such as a process (decompressionprocess) for decompressing the compressed information into originalinformation for a signal for which the transmission line decodingprocess has been carried out.

It is to be noted that, where the signal acquired through thetransmission line by the acquisition section 1101 has not been carriedout compression encoding, the information source decoding processingsection 1103 does not carry out the process of decompressing thecompressed information into the original information.

Here, as the decompression process, for example, MPEG decoding and soforth are available. Further, the transmission line decoding processsometimes includes descrambling in addition to the decompressionprocess.

In the reception system configured in such a manner as described above,the acquisition section 1101 receives a signal obtained by carrying outcompression encoding such as MPEG encoding for data of, for example,images, sound and so forth and further carrying out error correctionencoding such as LDPC encoding for the compression encoded data througha transmission line. The signal is supplied to the transmission linedecoding processing section 1102.

In the transmission line decoding processing section 1102, processessimilar to those carried out, for example, by the orthogonaldemodulation section 51, demapping section 52, deinterleaver 53 and LDPCdecoding section 56 (or LDPC decoding section 1021) are carried out asthe transmission line decoding process for the signal from theacquisition section 1101. Then, a signal obtained as a result of thetransmission line decoding process is supplied to the information sourcedecoding processing section 1103.

In the information source decoding processing section 1103, aninformation source decoding process such as MPEG decoding is carried outfor the signal from the transmission line decoding processing section1102, and an image or sound obtained as a result of the informationdecoding process is outputted.

Such a reception system of FIG. 148 as described above can be applied,for example, to a television tuner for receiving television broadcastingas digital broadcasting and so forth.

It is to be noted that it is possible to configure the acquisitionsection 1101, transmission line decoding processing section 1102 andinformation source decoding processing section 1103 each as anindependent apparatus (hardware (IC (Integrated Circuit) or the like) ora software module).

Further, as regards the acquisition section 1101, transmission linedecoding processing section 1102 and information source decodingprocessing section 1103, a set of the acquisition section 1101 andtransmission line decoding processing section 1102, another set of thetransmission line decoding processing section 1102 and informationsource decoding processing section 1103 or a further set of theacquisition section 1101, transmission line decoding processing section1102 and information source decoding processing section 1103 can beconfigured as a single independent apparatus.

FIG. 149 is a block diagram showing a second example of theconfiguration of the reception system which can be applied to thereception apparatus 12.

It is to be noted that, in FIG. 149, elements corresponding those inFIG. 148 are denoted by like reference numerals, and description of themis suitably omitted in the following description.

The reception system of FIG. 149 is common to that of FIG. 148 in thatit includes an acquisition section 1101, a transmission line decodingprocessing section 1102 and an information source decoding processingsection 1103 but is different from that of FIG. 148 in that it newlyincludes an outputting section 1111.

The outputting section 1111 is, for example, a display apparatus fordisplaying an image or a speaker for outputting sound and outputs animage, a sound of the like as a signal outputted from the informationsource decoding processing section 1103. In other words, the outputtingsection 1111 displays an image or outputs sound.

Such a reception system of FIG. 149 as described above can be applied,for example, to a TV (television receiver) for receiving a televisionbroadcast as a digital broadcast, a radio receiver for receiving a radiobroadcast and so forth.

It is to be noted that, where the signal acquired by the acquisitionsection 1101 is not in a form wherein compression encoding is notapplied, a signal outputted from the transmission line decodingprocessing section 1102 is supplied to the outputting section 1111.

FIG. 150 is a block diagram showing a third example of the configurationof the reception system which can be applied to the reception apparatus12.

It is to be noted that, in FIG. 150, corresponding elements to those ofFIG. 148 are denoted by like reference numerals, and in the followingdescription, description of them is suitably omitted.

The reception system of FIG. 150 is common to that of FIG. 148 in thatit includes an acquisition section 1101 and a transmission line decodingprocessing section 1102.

However, the reception system of FIG. 150 is different from that of FIG.148 in that it does not include the information source decodingprocessing section 1103 but newly includes a recording section 1121.

The recording section 1121 records (stores) a signal (for example, a TSpacket of a TS of MPEG) outputted from the transmission line decodingprocessing section 1102 on or into a recording (storage) medium such asan optical disk, a hard disk (magnetic disk) or a flash memory.

Such a reception system of FIG. 150 as described above can be applied toa recorder for recording a television broadcast or the like.

It is to be noted that, in FIG. 150, the reception system may includethe information source decoding processing section 1103 such that asignal after an information source decoding process has been carried outby the information source decoding processing section 1103, that is, animage or sound obtained by decoding, is recorded by the recordingsection 1121.

It should be understood by those skilled in the art that variousmodifications, combinations, sub-combinations and alterations may occurdepending on design requirements and other factors insofar as they arewithin the scope of the appended claims or the equivalents thereof.

1. An encoding apparatus for carrying out encoding by an LDPC (LowDensity Parity Check) code, comprising: a processor configured toperform encoding by an LDPC code which has a code length of 64,800 bitsand an encoding rate of 2/3; a parity check matrix of the LDPC codebeing configured such that elements of the value 1 of an informationmatrix, which corresponds to the code length of the parity check matrixand an information length corresponding to the encoding rate, decided bya parity check matrix initial value table representative of thepositions of the elements of the value 1 of the information matrix arearranged in a period of every 360 columns in the column direction; theparity check matrix value table being formed from 317 2255 2324 27233538 3576 6194 6700 9101 10057 12739 17407 21039 1958 2007 3294 439412762 14505 14593 14692 16522 17737 19245 21272 21379 127 860 5001 56338644 9282 12690 14644 17553 19511 19681 20954 21002 2514 2822 5781 62978063 9469 9551 11407 11837 12985 15710 20236 20393 1565 3106 4659 49266495 6872 7343 8720 15785 16434 16727 19884 21325 706 3220 8568 1089612486 13663 16398 16599 19475 19781 20625 20961 21335 4257 10449 1240614561 16049 16522 17214 18029 18033 18802 19062 19526 20748 412 433 5582614 2978 4157 6584 9320 11683 11819 13024 14486 16860 777 5906 74038550 8717 8770 11436 12846 13629 14755 15688 16392 16419 4093 5045 60377248 8633 9771 10260 10809 11326 12072 17516 19344 19938 2120 2648 31553852 6888 12258 14821 15359 16378 16437 17791 20614 21025 1085 2434 58167151 8050 9422 10884 12728 15353 17733 18140 18729 20920 856 1690 127876532 7357 9151 4210 16615 18152 11494 14036 17470 2474 10291 10323 17786973 10739 4347 9570 18748 2189 11942 20666 3868 7526 17706 8780 1479618268 160 16232 17399 1285 2003 18922 4658 17331 20361 2765 4862 58754565 5521 8759 3484 7305 15829 5024 17730 17879 7031 12346 15024 1796365 11352 2490 3143 5098 2643 3101 21259 4315 4724 13130 594 1736518322 5983 8597 9627 10837 15102 20876 10448 20418 21478 3848 1202915228 708 5652 13146 5998 7534 16117 2098 13201 18317 9186 14548 177765246 10398 18597 3083 4944 21021 13726 18495 19921 6736 10811 1754510084 12411 14432 1064 13555 17033 679 9878 13547 3422 9910 20194 36403701 10046 5862 10134 11498 5923 9580 15060 1073 3012 16427 5527 2011320883 7058 12924 15151 9764 12230 17375 772 7711 12723 555 13816 1537610574 11268 17932 15442 17266 20482 390 3371 8781 10512 12216 17180 430914068 15783 3971 11673 20009 9259 14270 17199 2947 5852 20101 3965 972215363 1429 5689 16771 6101 6849 12781 3676 9347 18761 350 11659 183425961 14803 16123 2113 9163 13443 2155 9808 12885 2861 7988 11031 73099220 20745 6834 8742 11977 2133 12908 14704 10170 13809 18153 1346414787 14975 799 1107 3789 3571 8176 10165 5433 13446 15481 3351 676712840 8950 8974 11650 1430 4250 21332 6283 10628 15050 8632 14404 169166509 10702 16278 15900 16395 17995 8031 18420 19733 3747 4634 17087 44536297 16262 2792 3513 17031 14846 20893 21563 17220 20436 21337 275 410710497 3536 7520 10027 14089 14943 19455 1965 3931 21104 2439 11565 17932154 15279 21414 10017 11269 16546 7169 10161 16928 10284 16791 20655 363175 8475 2605 16269 19290 8947 9178 15420 5687 9156 12408 8096 973814711 4935 8093 19266 2667 10062 15972 6389 11318 14417 8800 18137 184345824 5927 15314 6056 13168 15179 3284 13138 18919 13115 17259
 17332. 2.An encoding method for an encoding apparatus which carries out encodingby an LDPC (Low Density Parity Check) code, comprising: performing, by aprocessor of the encoding apparatus, encoding by an LDPC code which hasa code length of 64,800 bits and an encoding rate of 2/3; a parity checkmatrix of the LDPC code being configured such that elements of the value1 of an information matrix, which corresponds to the code length of theparity check matrix and an information length corresponding to theencoding rate, decided by a parity check matrix initial value tablerepresentative of the positions of the elements of the value 1 of theinformation matrix are arranged in a period of every 360 columns in thecolumn direction; the parity check matrix initial value table beingformed from 317 2255 2324 2723 3538 3576 6194 6700 9101 10057 1273917407 21039 1958 2007 3294 4394 12762 14505 14593 14692 16522 1773719245 21272 21379 127 860 5001 5633 8644 9282 12690 14644 17553 1951119681 20954 21002 2514 2822 5781 6297 8063 9469 9551 11407 11837 1298515710 20236 20393 1565 3106 4659 4926 6495 6872 7343 8720 15785 1643416727 19884 21325 706 3220 8568 10896 12486 13663 16398 16599 1947519781 20625 20961 21335 4257 10449 12406 14561 16049 16522 17214 1802918033 18802 19062 19526 20748 412 433 558 2614 2978 4157 6584 9320 1168311819 13024 14486 16860 777 5906 7403 8550 8717 8770 11436 12846 1362914755 15688 16392 16419 4093 5045 6037 7248 8633 9771 10260 10809 1132612072 17516 19344 19938 2120 2648 3155 3852 6888 12258 14821 15359 1637816437 17791 20614 21025 1085 2434 5816 7151 8050 9422 10884 12728 1535317733 18140 18729 20920 856 1690 12787 6532 7357 9151 4210 16615 1815211494 14036 17470 2474 10291 10323 1778 6973 10739 4347 9570 18748 218911942 20666 3868 7526 17706 8780 14796 18268 160 16232 17399 1285 200318922 4658 17331 20361 2765 4862 5875 4565 5521 8759 3484 7305 158295024 17730 17879 7031 12346 15024 179 6365 11352 2490 3143 5098 26433101 21259 4315 4724 13130 594 17365 18322 5983 8597 9627 10837 1510220876 10448 20418 21478 3848 12029 15228 708 5652 13146 5998 7534 161172098 13201 18317 9186 14548 17776 5246 10398 18597 3083 4944 21021 1372618495 19921 6736 10811 17545 10084 12411 14432 1064 13555 17033 679 987813547 3422 9910 20194 3640 3701 10046 5862 10134 11498 5923 9580 150601073 3012 16427 5527 20113 20883 7058 12924 15151 9764 12230 17375 7727711 12723 555 13816 15376 10574 11268 17932 15442 17266 20482 390 33718781 10512 12216 17180 4309 14068 15783 3971 11673 20009 9259 1427017199 2947 5852 20101 3965 9722 15363 1429 5689 16771 6101 6849 127813676 9347 18761 350 11659 18342 5961 14803 16123 2113 9163 13443 21559808 12885 2861 7988 11031 7309 9220 20745 6834 8742 11977 2133 1290814704 10170 13809 18153 13464 14787 14975 799 1107 3789 3571 8176 101655433 13446 15481 3351 6767 12840 8950 8974 11650 1430 4250 21332 628310628 15050 8632 14404 16916 6509 10702 16278 15900 16395 17995 803118420 19733 3747 4634 17087 4453 6297 16262 2792 3513 17031 14846 2089321563 17220 20436 21337 275 4107 10497 3536 7520 10027 14089 14943 194551965 3931 21104 2439 11565 17932 154 15279 21414 10017 11269 16546 716910161 16928 10284 16791 20655 36 3175 8475 2605 16269 19290 8947 917815420 5687 9156 12408 8096 9738 14711 4935 8093 19266 2667 10062 159726389 11318 14417 8800 18137 18434 5824 5927 15314 6056 13168 15179 328413138 18919 13115 17259 17332.